Skip to main content Accessibility help
×
Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-18T19:21:10.322Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  01 June 2011

Jouko Väänänen
Affiliation:
University of Helsinki and University of Amsterdam
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Models and Games , pp. 353 - 361
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aczel, P. 1977. An introduction to inductive definitions. Pages 739–783 of: Barwise, Jon (ed), Handbook of Mathematical Logic. Amsterdam: North–Holland Publishing Co. Cited on page 125.Google Scholar
Barwise, J. 1969. Remarks on universal sentences of. Duke Mathematical Journal, 36, 631–637. Cited on page 223.CrossRefGoogle Scholar
Barwise, J. 1975. Admissible Sets and Structures. Berlin: Springer-Verlag. Perspectives in Mathematical Logic. Cited on pages 71, 76, 171, and 204.CrossRefGoogle Scholar
Barwise, J. 1976. Some applications of Henkin quantifiers. Israel Journal of Mathematics, 25(1–2), 47–63. Cited on page 204.CrossRefGoogle Scholar
Barwise, J. and Cooper, R. 1981. Generalized quantifiers and natural language. Linguistics and Philosophy, 159–219. Cited on page 343.CrossRefGoogle Scholar
Barwise, J., and Feferman, S. (eds). 1985. Model-Theoretic Logics. Perspectives in Mathematical Logic. New York: Springer-Verlag. Cited on pages 118, 126, and 343.Google Scholar
Barwise, J., Kaufmann, M., and Makkai, M. 1978. Stationary logic. Annals of Mathematical Logic, 13(2), 171–224. Cited on page 343.CrossRefGoogle Scholar
Bell, J. L., and Slomson, A. B. 1969. Models and Ultraproducts: An Introduction. Amsterdam: North-Holland Publishing Co. Cited on page 126.Google Scholar
Benda, M. 1969. Reduced products and nonstandard logics. Journal of Symbolic Logic, 34, 424–436. Cited on pages 125, 126, 238, and 275.CrossRefGoogle Scholar
Beth, E. W. 1953. On Padoa's method in the theory of definition. Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes Mathematicae, 15, 330–339. Cited on page 126.CrossRefGoogle Scholar
Beth, E. W. 1955a. Remarks on natural deduction. Nederl. Akad. Wetensch. Proc. Ser. A. 58 = Indagationes Mathematicae, 17, 322–325. Cited on page 125.CrossRefGoogle Scholar
Beth, E. W. 1955b. Semantic Entailment and Formal Derivability. Mededelingen der koninklijke Nederlandse Akademie van Wetenschappen, afd. Letterkunde. Nieuwe Reeks, Deel 18, No. 13. N. V. Noord-Hollandsche Uitgevers Maatschappij, Amsterdam. Cited on page 125.
Bissell-Siders, R. 2007. Ehrenfeucht-Fraïssé games on linear orders. Pages 72–82 of: Logic, Language, Information and Computation. Lecture Notes in Computer Scence, vol. 4576. Berlin: Springer. Cited on page 126.Google Scholar
Brown, J., and Hoshino, R. 2007. The Ehrenfeucht-Fraïssé game for paths and cycles. Ars Combinatoria, 83, 193–212. Cited on page 126.Google Scholar
Burgess, J. 1977. Descriptive set theory and infinitary languages. Zbornik Radova Matematički Institut Beograd (Nova Serija), 2(10), 9–30. Set Theory, Foundations of Mathematics (Proc. Sympos., Belgrade, 1977). Cited on page 222.Google Scholar
Burgess, J. 1978. On the Hanf number of Souslin logic. Journal of Symbolic Logic, 43(3), 568–571. Cited on page 223.CrossRefGoogle Scholar
Caicedo, X. 1980. Back-and-forth systems for arbitrary quantifiers. Pages 83–102 of: Mathematical logic in Latin America (Proc. IV Latin Amer. Sympos. Math. Logic, Santiago, 1978). Stud. Logic Foundations Math., vol. 99. Amsterdam: North-Holland. Cited on page 343.Google Scholar
Calais, J.-P. 1972. Partial isomorphisms and infinitary languages. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 18, 435–456. Cited on page 275.CrossRefGoogle Scholar
Cantor, G. 1895. Beiträge zur Begründung der transfiniten Mengenlehre, I. Mathematische Annalen, 46, 481–512. Cited on page 65.CrossRefGoogle Scholar
Chang, C. C. 1968. Infinitary properties of models generated from indiscernibles. Pages 9–21 of: Logic, Methodology and Philos. Sci. III (Proc. Third Internat. Congr., Amsterdam, 1967). Amsterdam: North-Holland. Cited on page 275.Google Scholar
Chang, C. C., and Keisler, H. J. 1990. Model theory. Third edn. Studies in Logic and the Foundations of Mathematics, vol. 73. Amsterdam: North-Holland Publishing Co. Cited on pages 125, 203, 246, 248, and 342.Google Scholar
Craig, W. 1957a. Linear reasoning. A new form of the Herbrand-Gentzen theorem. Journal of Symbolic Logic, 22, 250–268. Cited on page 126.CrossRefGoogle Scholar
Craig, W. 1957b. Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory. Journal of Symbolic Logic, 22, 269–285. Cited on page 126.CrossRefGoogle Scholar
Craig, W. 2008. The road to two theorems of logic. Synthese, 164(3), 333–339. Cited on page 126.CrossRefGoogle Scholar
Devlin, K. 1993. The Joy of Sets. Second edn. New York: Springer-Verlag. Cited on page 11.CrossRefGoogle Scholar
Dickmann, M. A. 1975. Large Infinitary Languages. Amsterdam: North-Holland Publishing Co. Model theory, Studies in Logic and the Foundations of Mathematics, Vol. 83. Cited on pages 171, 244, and 275.Google Scholar
Dickmann, M. A. 1985. Larger infinitary languages. Pages 317–363 of: Model-Theoretic Logics. Perspect. Math. Logic. New York: Springer. Cited on page 275.Google Scholar
Džamonja, M., and Väänänen, J. 2004. A family of trees with no uncountable branches. Topology Proceedings, 28(1), 113–132. Cited on page 276.Google Scholar
Ehrenfeucht, A. 1957. Application of games to some problems of mathematical logic. Bulletin de l'Acadámie Polonaise des Science, Série des Sciences Mathématiques, Astronomiques et Physiques Cl. III., 5, 35–37, IV. Cited on pages 48 and 71.Google Scholar
Ehrenfeucht, A. 1960/1961. An application of games to the completeness problem for formalized theories. Fundamenta Mathematicae, 49, 129–141. Cited on pages 48 and 71.CrossRefGoogle Scholar
Eklof, P., Foreman, M., and Shelah, S. 1995. On invariants for ω1-separable groups. Transactions of the American Mathematical Society, 347(11), 4385–4402. Cited on page 277.Google Scholar
Ellentuck, E. 1975. The foundations of Suslin logic. Journal of Symbolic Logic, 40(4), 567–575. Cited on page 210.CrossRefGoogle Scholar
Ellentuck, E. 1976. Categoricity regained. Journal of Symbolic Logic, 41(3), 639–643. Cited on page 71.CrossRefGoogle Scholar
Enderton, H. 1970. Finite partially-ordered quantifiers. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 16, 393–397. Cited on page 207.CrossRefGoogle Scholar
Enderton, H. 1977. Elements of Set Theory. New York: Academic Press [Harcourt Brace Jovanovich Publishers]. Cited on page 11.Google Scholar
Enderton, H. 2001. A Mathematical Introduction to Logic. Second edn. Harcourt/Academic Press, Burlington, MA. Cited on page 102.Google Scholar
Fagin, R. 1976. Probabilities on finite models. Journal of Symbolic Logic, 41(1), 50–58. Cited on page 48.CrossRefGoogle Scholar
Fraïssé, R. 1955. Sur quelques classifications des relations, basées sur des isomorphismes restreints. II. Application aux relations d'ordre, et construction d'exemples montrant que ces classifications sont distinctes. Publ. Sci. Univ. Alger. Sér. A., 2, 273–295 (1957). Cited on pages 71 and 125.Google Scholar
Fuhrken, G. 1964. Skolem-type normal forms for first-order languages with a generalized quantifier. Fundamenta Mathematicae, 54, 291–302. Cited on page 343.CrossRefGoogle Scholar
Gaifman, H. 1964. Concerning measures in first order calculi. Israel Journal for Mathematics, 2, 1–18. Cited on page 48.CrossRefGoogle Scholar
Gale, David, and Stewart, F. M. 1953. Infinite games with perfect information. Pages 245–266 of: Contributions to the Theory of Games, vol. 2. Annals of Mathematics Studies, no. 28. Princeton, N. J.: Princeton University Press. Cited on page 28.Google Scholar
Gentzen, G. 1934. Untersuchungenüber das logische Schließen. I. Mathematische Zeitschrift, 39, 176–210. Cited on page 125.CrossRefGoogle Scholar
Gentzen, G. 1969. The Collected Papers of Gerhard Gentzen. Edited by M. E., Szabo. Studies in Logic and the Foundations of Mathematics. Amsterdam: North-Holland Publishing Co. Cited on page 125.Google Scholar
Gostanian, R., and Hrbáček, K. 1976. On the failure of the weak Beth property. Proceedings of the American Mathematical Society, 58, 245–249. Cited on page 245.CrossRefGoogle Scholar
Grädel, E., Kolaitis, P. G., Libkin, L., Marx, M., Spencer, J., Vardi, M. Y., Venema, Y., and Weinstein, S. 2007. Finite Model Theory and its Applications. Texts in Theoretical Computer Science. An EATCS Series. Berlin: Springer. Cited on page 48.Google Scholar
Green, J. 1975. Consistency properties for finite quantifier languages. Pages 73–123. Lecture Notes in Math., Vol. 492 of: Infinitary Logic: in Memoriam Carol Karp. Berlin: Springer. Cited on page 222.Google Scholar
Green, J. 1978. κ-Suslin logic. Journal of Symbolic Logic, 43(4), 659–666. Cited on page 223.CrossRefGoogle Scholar
Green, J. 1979. Some model theory for game logics. Journal of Symbolic Logic, 44(2), 147–152. Cited on pages 210 and 223.CrossRefGoogle Scholar
Gurevich, Y. 1984. Toward logic tailored for computational complexity. Pages 175–216 of: Computation and Proof Theory (Aachen, 1983). Lecture Notes in Math., vol. 1104. Berlin: Springer-Verlag. Cited on page 126.Google Scholar
Hájek, P. 1976. Some remarks on observational model-theoretic languages. Pages 335–345 of: Set Theory and Hierarchy Theory (Proc. Second Conf., Bierutowice, 1975), Lecture Notes in Math., Vol. 537. Berlin: Springer. Cited on pages 126 and 343.Google Scholar
Harnik, V., and Makkai, M. 1976. Applications of Vaught sentences and the covering theorem. Journal of Symbolic Logic, 41(1), 171–187. Cited on page 222.CrossRefGoogle Scholar
Härtig, K. 1965. Über einen Quantifikator mit zwei Wirkungsbereichen. Pages 31–36 of: Colloq. Found. Math., Math. Machines and Appl. (Tihany, 1962). Budapest: Akad. Kiadó. Cited on page 343.Google Scholar
Hella, L. 1989. Definability hierarchies of generalized quantifiers. Annals of Pure and Applied Logic, 43(3), 235–271. Cited on page 343.CrossRefGoogle Scholar
Hella, L., and Sandu, G. 1995. Partially ordered connectives and finite graphs. Pages 79–88 of: Krynicki, M., M., Mostowski, and L., Szczerba (eds), Quantifiers: Logics, Models and Computation, Vol. II. Kluwer. Cited on page 343.Google Scholar
Henkin, L. 1961. Some remarks on infinitely long formulas. Pages 167–183 of: Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959). Oxford: Pergamon. Cited on pages 125 and 204.Google Scholar
Herre, H., Krynicki, M., Pinus, A., and Väänänen, J. 1991. The Härtig quantifier: a survey. Journal of Symbolic Logic, 56(4), 1153–1183. Cited on page 343.CrossRefGoogle Scholar
Hintikka, J. 1953. Distributive normal forms in the calculus of predicates. Acta Philosophica Fennica, 6, 71. Cited on page 48.Google Scholar
Hintikka, J. 1955. Form and content in quantification theory. Acta Philosophica Fennica, 8, 7–55. Cited on page 125.Google Scholar
Hintikka, J. 1968. Language-games for quantifiers. Pages 46–73 of: N., Rescher (ed.), Studies in Logical Lheory, Oxford: Blackwell Publishers. Cited on page 125.Google Scholar
Hintikka, J., and Rantala, V. 1976. A new approach to infinitary languages. Annals of Mathematical Logic, 10(1), 95–115. Cited on page 276.CrossRefGoogle Scholar
Hodges, W. 1985. Building Models by Games. London Mathematical Society Student Texts, vol. 2. Cambridge: Cambridge University Press. Cited on page 126.Google Scholar
Hodges, W. 1993. Model Theory. Encyclopedia of Mathematics and its Applications, vol. 42. Cambridge: Cambridge University Press. Cited on page 125.CrossRefGoogle Scholar
Huuskonen, T. 1995. Comparing notions of similarity for uncountable models. Journal of Symbolic Logic, 60(4), 1153–1167. Cited on pages 276 and 278.CrossRefGoogle Scholar
Huuskonen, T., Hyttinen, T., and Rautila, M. 2004. On potential isomorphism and non-structure. Archive für mathematische Logic, 43(1), 85–120. Cited on page 277.Google Scholar
Hyttinen, T. 1987. Games and infinitary languages. Annales Academi Scientiarum Fennic Series A I Mathematica Dissertationes, 32. Cited on pages 275, 276, and 277.Google Scholar
Hyttinen, T. 1990. Model theory for infinite quantifier languages. Fundamenta Mathematicae, 134(2), 125–142. Cited on pages 275 and 276.CrossRefGoogle Scholar
Hyttinen, T. 1992. On nondetermined Ehrenfeucht-Fraïssé games and unstable theories. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 38(4), 399–408. Cited on page 277.CrossRefGoogle Scholar
Hyttinen, T., and Rautila, M. 2001. The canary tree revisited. Journal of Symbolic Logic, 66(4), 1677–1694. Cited on page 277.CrossRefGoogle Scholar
Hyttinen, T., and Shelah, S. 1999. Constructing strongly equivalent nonisomorphic models for unsuperstable theories. Part C. Journal of Symbolic Logic, 64(2), 634–642. Cited on page 277.CrossRefGoogle Scholar
Hyttinen, T., Shelah, S., and Tuuri, H. 1993. Remarks on strong nonstructure theorems. Notre Dame J. Formal Logic, 34(2), 157–168. Cited on page 277.CrossRefGoogle Scholar
Hyttinen, T., Shelah, S., and Väänänen, J. 2002. More on the Ehrenfeucht-Fraïssé-game of length ω1. Fundamenta Mathematicae, 175(1), 79–96. Cited on page 277.CrossRefGoogle Scholar
Hyttinen, T., and Tuuri, H. 1991. Constructing strongly equivalent nonisomorphic models for unstable theories. Annals of Pure and Applied Logic, 52(3), 203–248. Cited on pages 275 and 276.CrossRefGoogle Scholar
Hyttinen, T., and Väänänen, J. 1990. On Scott and Karp trees of uncountable models. Journal of Symbolic Logic, 55(3), 897–908. Cited on pages 255, 275, 276, and 277.CrossRefGoogle Scholar
Jech, T. 1997. Set theory. Second edn. Perspectives in Mathematical Logic. Berlin: Springer-Verlag. Cited on pages 11, 24, 28, 59, 61, and 189.CrossRefGoogle Scholar
Juhász, I., and Weiss, W. 1978. On a problem of Sikorski. Fundamenta Mathematicae, 100(3), 223–227. Cited on page 277.CrossRefGoogle Scholar
Karp, C. 1964. Languages with Expressions of Infinite Length. Amsterdam: North-Holland Publishing Co. Cited on page 171.Google Scholar
Karp, C. 1965. Finite-quantifier equivalence. Pages 407–412 of: Theory of Models (Proc. 1963 Internat. Sympos. Berkeley). Amsterdam: North-Holland. Cited on pages 71 and 171.Google Scholar
Karttunen, M. 1979. Infinitary languages N∞λ and generalized partial isomorphisms. Pages 153–168 of: Essays on Mathematical and Philosophical Logic (Proc. Fourth Scandinavian Logic Sympos. and First Soviet-Finnish Logic Conf., Jyväskylä, 1976). Synthese Library, vol. 122. Dordrecht: Reidel. Cited on page 276.Google Scholar
Karttunen, M. 1984. Model theory for infinitely deep languages. Annales Academiae Scientiarum Fennicae Series A I Mathematica Dissertationes, 96. Cited on pages 275 and 276.Google Scholar
Keisler, H. J., and Morley, M. 1968. Elementary extensions of models of set theory. Israel Journal for Mathematics, 6, 49–65. Cited on page 126.CrossRefGoogle Scholar
Keisler, H. J. 1965. Finite approximations of infinitely long formulas. Pages 158–169 of: Theory of Models (Proc. 1963 Internat. Sympos. Berkeley). Amsterdam: North-Holland. Cited on page 222.Google Scholar
Keisler, H. J. 1970. Logic with the quantifier “there exist uncountably many”. Annals of Mathematical Logic, 1, 1–93. Cited on pages 314 and 343.CrossRefGoogle Scholar
Keisler, H. J. 1971. Model Theory for Infinitary Logic. Amsterdam: North-Holland Publishing Co. Studies in Logic and the Foundations of Mathematics, Vol. 62. Cited on pages 171 and 222.Google Scholar
Kolaitis, P., and Väänänen, J. 1995. Generalized quantifiers and pebble games on finite structures. Annals of Pure and Applied Logic, 74(1), 23–75. Cited on page 343.CrossRefGoogle Scholar
Kolaitis, P., and Vardi, M. 1992. Infinitary logics and 0-1 laws. Information and Computation, 98(2), 258–294. Selections from the 1990 IEEE Symposium on Logic in Computer Science. Cited on page 48.CrossRefGoogle Scholar
Krynicki, M., Mostowski, M., and Szczerba, L. (Eds.). 1995. Quantifiers. Berlin: Kluwer Academic Publishers. Cited on page 343.Google Scholar
Kueker, D. 1968. Definability, automorphisms and infinitary languages. Pages 152–165 of: The Syntax and Semantics of Infinitary Languages. Springer Lecture Notes in Math., Vol. 72. Berlin: Springer-Verlag. Cited on page 171.Google Scholar
Kueker, D. 1972. Löwenheim-Skolem and interpolation theorems in infinitary languages. Bulletin of the American Mathematical Society, 78, 211–215. Cited on pages 125 and 222.CrossRefGoogle Scholar
Kueker, D. 1975. Back-and-forth arguments and infinitary logics. Pages 17–71 of: Infinitary Logic: in Memoriam Carol Karp. Lecture Notes in Math., Vol. 492. Berlin: Springer-Verlag. Cited on pages 171 and 275.CrossRefGoogle Scholar
Kueker, D. 1977. Countable approximations and Löwenheim-Skolem theorems. Annals of Mathematical Logic, 11(1), 57–103. Cited on pages 85, 125, and 222.CrossRefGoogle Scholar
Kuratowski, K. 1966. Topology. Vol. I. New edition, revised and augmented. Translated from the French by J., Jaworowski. New York: Academic Press. Cited on page 223.Google Scholar
Kurepa, G. 1956. Ensembles ordonnés et leurs sous-ensembles bien ordonnés. Les Comptes Rendus de l'Académie des sciences, 242, 2202–2203. Cited on pages 255, 275, and 278.Google Scholar
Lindström, P. 1966. First order predicate logic with generalized quantifiers. Theoria, 32, 186–195. Cited on page 342.Google Scholar
Lindström, P. 1973. A characterization of elementary logic. Pages 189–191 of: Modality, Morality and Other Problems of Sense and Nonsense. Lund: CWK Gleerup Bokförlag. Cited on pages 112 and 126.Google Scholar
Lopez-Escobar, E. G. K. 1965. An interpolation theorem for denumerably long formulas. Fundamenta Mathematicae, 57, 253–272. Cited on pages 222 and 223.CrossRefGoogle Scholar
Lopez-Escobar, E. G. K. 1966a. An addition to: “On defining well-orderings”. Fundamenta Mathematicae, 59, 299–300. Cited on page 222.CrossRefGoogle Scholar
Lopez-Escobar, E. G. K. 1966b. On defining well-orderings. Fundamenta Mathematicae, 59, 13–21. Cited on pages 183 and 222.CrossRefGoogle Scholar
Lorenzen, P. 1961. Ein dialogisches Konstruktivitätskriterium. Pages 193–200 of: Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959). Oxford: Pergamon. Cited on page 125.Google Scholar
Łoś, J. 1955. Quelques remarques, théorèmes et problèmes sur les classes définissables d'algèbres. Pages 98–113 of: Mathematical Interpretation of Formal Systems. Amsterdam: North-Holland Publishing Co. Cited on page 126.Google Scholar
Löwenheim, L. 1915. Über Möglichkeiten im Relativkalkul. Mathematische Annalen, 76, 447–470. Cited on page 125.CrossRefGoogle Scholar
Luosto, K. 2000. Hierarchies of monadic generalized quantifiers. Journal of Symbolic Logic, 65(3), 1241–1263. Cited on page 343.CrossRefGoogle Scholar
Makkai, M. 1969a. An application of a method of Smullyan to logics on admissible sets. Bulletin de l'Acadámie Polonaise des Science, Série des Sciences Mathématiques, Astronomiques et Physiques, 17, 341–346. Cited on page 222.Google Scholar
Makkai, M. 1969b. On the model theory of denumerably long formulas with finite strings of quantifiers. Journal of Symbolic Logic, 34, 437–459. Cited on pages 222 and 223.CrossRefGoogle Scholar
Makkai, M. 1977. Admissible sets and infinitary logic. Pages 233–281 of: Handbook of Mathematical Logic, Studies in Logic and the Foundations of Math., Vol. 90. Amsterdam: North-Holland. Cited on pages 171, 213, and 222.Google Scholar
Makowsky, J. A., and Shelah, S. 1981. The theorems of Beth and Craig in abstract model theory. II. Compact logics. Archiv für mathematische Logik und Grundlagenforschung, 21(1–2), 13–35. Cited on page 343.CrossRefGoogle Scholar
Malitz, J. 1969. Universal classes in infinitary languages. Duke Mathematical Journal, 36, 621–630. Cited on page 223.CrossRefGoogle Scholar
Mekler, A., and Oikkonen, J. 1993. Abelian p-groups with no invariants. Journal of Pure and Applied Algebra, 87(1), 51–59. Cited on page 277.CrossRefGoogle Scholar
Mekler, A., and Shelah, S. 1986. Stationary logic and its friends. II. Notre Dame Journal of Formal Logic, 27(1), 39–50. Cited on page 343.CrossRefGoogle Scholar
Mekler, A., and Shelah, S. 1993. The canary tree. Canadian Mathematical Bulletin, 36(2), 209–215. Cited on page 277.CrossRefGoogle Scholar
Mekler, A., Shelah, S., and Väänänen, J. 1993. The Ehrenfeucht–Fraïssé game of length ω1. Transactions of the American Mathematical Society, 339(2), 567–580. Cited on pages 253 and 277.Google Scholar
Mekler, A., and Väänänen, J. 1993. Trees and -subsets of. Journal of Symbolic Logic, 58(3), 1052–1070. Cited on pages 273, 276, and 277.CrossRefGoogle Scholar
Mildenberger, H. 1992. On the homogeneity property for certain quantifier logics. Archive für mathematische Logic, 31(6), 445–455. Cited on page 343.CrossRefGoogle Scholar
Morley, M. 1968. Partitions and models. Pages 109–158 of: Proceedings of the Summer School in Logic (Leeds, 1967). Berlin: Springer. Cited on pages 126 and 222.Google Scholar
Morley, M. 1970. The number of countable models. Journal of Symbolic Logic, 35, 14–18. Cited on page 152.CrossRefGoogle Scholar
Morley, M., and Vaught, R. 1962. Homogeneous universal models. Mathematica Scandinavica, 11, 37–57. Cited on page 343.CrossRefGoogle Scholar
Mortimer, M. 1975. On languages with two variables. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 21, 135–140. Cited on page 38.CrossRefGoogle Scholar
Moschovakis, Y. 1972. The game quantifier. Proceedings of the American Mathematical Society, 31, 245–250. Cited on page 201.CrossRefGoogle Scholar
Mostowski, A. 1957. On a generalization of quantifiers. Fundamenta Mathematicae, 44, 12–36. Cited on pages 291, 314, and 342.CrossRefGoogle Scholar
Mycielski, J. 1992. Games with perfect information. Pages 41–70 of: Handbook of Game Theory with Economic Applications, Vol. I. Handbooks in Econom., vol. 11. Amsterdam: North-Holland. Cited on page 28.Google Scholar
Nadel, M., and Stavi, J. 1978. L∞λ-equivalence, isomorphism and potential isomorphism. Transactions of the American Mathematical Society, 236, 51–74. Cited on page 277.Google Scholar
Nešetřil, J., and Väänänen, J. 1996. Combinatorics and quantifiers. Commentationes Mathematicae Universitatis Carolinae, 37(3), 433–443. Cited on page 343.Google Scholar
Oikkonen, J. 1990. On Ehrenfeucht–Fraïssé equivalence of linear orderings. Journal of Symbolic Logic, 55(1), 65–73. Cited on page 275.CrossRefGoogle Scholar
Oikkonen, J. 1997. Undefinability of κ-well-orderings in L∞κ. Journal of Symbolic Logic, 62(3), 999–1020. Cited on page 276.CrossRefGoogle Scholar
Peters, S., and Westerståhl, D. 2008. Quantifiers in Language and Logic. Oxford: Oxford University Press. Cited on page 343.CrossRefGoogle Scholar
Rantala, V. 1981. Infinitely deep game sentences and interpolation. Acta Philosophica Fennica, 32, 211–219. Cited on page 276.Google Scholar
Rosenstein Joseph, G. 1982. Linear Orderings. Pure and Applied Mathematics, vol. 98. New York: Academic Press Inc. [Harcourt Brace Jovanovich Publishers]. Cited on page 71.Google Scholar
Rotman, B., and Kneebone, G. T. 1966. The Theory of Sets and Transfinite Numbers. London: Oldbourne. Cited on page 11.Google Scholar
Schwalbe, U., and Walker, P. 2001. Zermelo and the early history of game theory. Games and Economomic Behaviour, 34(1), 123–137. With an appendix by Ernst Zermelo, translated from German by the authors. Cited on page 28.CrossRefGoogle Scholar
Scott, D. 1965. Logic with denumerably long formulas and finite strings of quantifiers. Pages 329–341 of: Theory of Models (Proc. 1963 Internat. Sympos. Berkeley). Amsterdam: North-Holland. Cited on page 171.Google Scholar
Scott, D., and Tarski, A. 1958. The sentential calculus with infinitely long expressions. Colloqium Mathematicum, 6, 165–170. Cited on page 170.CrossRefGoogle Scholar
Shelah, S. 1971. Every two elementarily equivalent models have isomorphic ultrapowers. Israel Journal for Mathematics, 10, 224–233. Cited on page 125.CrossRefGoogle Scholar
Shelah, S. 1975. Generalized quantifiers and compact logic. Transactions of the American Mathematical Society, 204, 342–364. Cited on page 343.CrossRefGoogle Scholar
Shelah, S. 1985. Remarks in abstract model theory. Annals of Pure and Applied Logic, 29(3), 255–288. Cited on page 343.CrossRefGoogle Scholar
Shelah, S. 1990. Classification theory and the number of nonisomorphic models. Second edn. Studies in Logic and the Foundations of Mathematics, vol. 92. Amsterdam: North-Holland Publishing Co. Cited on pages 241, 275, and 276.Google Scholar
Shelah, S., and Väänänen, J. 2000. Stationary sets and infinitary logic. Journal of Symbolic Logic, 65(3), 1311–1320. Cited on page 277.CrossRefGoogle Scholar
Shelah, S., and Väisänen, P. 2002. Almost free groups and Ehrenfeucht–Fraïssé games for successors of singular cardinals. Annals of Pure and Applied Logic, 118(1–2), 147–173. Cited on page 277.CrossRefGoogle Scholar
Sierpiński, W. 1933. Sur un problème de la théorie des rélations. Annali della Scuola Normale Superiore di Pisa, II. Ser., 2, 285–287. Cited on page 223.Google Scholar
Sikorski, R. 1950. Remarks on some topological spaces of high power. Fundamenta Mathematicae, 37, 125–136. Cited on page 277.CrossRefGoogle Scholar
Skolem, T. 1923. Einige Bemerkungen zur axiomatischen Begündung der Mengenlehre. Pages 217–232 of: 5. Kongreß Skandinav. in Helsingfors vom 4. bis 7. Juli 1922 (Akademische Buchhandlung). Cited on page 125.
Skolem, T. 1970. Selected Works in Logic. Edited by Jens Erik, Fenstad. Oslo: Universitetsforlaget. Cited on page 125.Google Scholar
Smullyan, R. 1963. A unifying principal in quantification theory. Proceedings of the National Academy of Sciences U.S.A., 49, 828–832. Cited on page 125.CrossRefGoogle ScholarPubMed
Smullyan, R. 1968. First-Order Logic. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 43. New York: Springer-Verlag New York, Inc. Cited on page 125.CrossRefGoogle Scholar
Spencer, J. 2001. The Strange Logic of Random Graphs. Algorithms and Combinatorics, vol. 22. Berlin: Springer-Verlag. Cited on page 48.CrossRefGoogle Scholar
Svenonius, L. 1965. On the denumerable models of theories with extra predicates. Pages 376–389 of: Theory of Models (Proc. 1963 Internat. Sympos. Berkeley). Amsterdam: North-Holland. Cited on page 208.Google Scholar
Tarski, A. 1958. Remarks on predicate logic with infinitely long expressions. Colloqium Mathematicum, 6, 171–176. Cited on page 170.CrossRefGoogle Scholar
Todorčević, S. 1981a. Stationary sets, trees and continuums. Publications de l'Institut Mathématique, 29(43), 249–262. Cited on page 278.Google Scholar
Todorčević, S. 1981b. Trees, subtrees and order types. Annals of Mathematical Logic, 20(3), 233–268. Cited on page 277.CrossRefGoogle Scholar
Todorčević, S., and Väänänen, J. 1999. Trees and Ehrenfeucht–Fraïssé games. Annals of Pure and Applied Logic, 100(1–3), 69–97. Cited on pages 255, 258, and 276.CrossRefGoogle Scholar
Tuuri, H. 1990. Infinitary languages and Ehrenfeucht–Fraïssé games. PhD in Mathematics, University of Helsinki. Cited on page 276.Google Scholar
Tuuri, H. 1992. Relative separation theorems for. Notre Dame Journal of Formal Logic, 33(3), 383–401. Cited on page 276.CrossRefGoogle Scholar
Väänänen, J. 1977. Remarks on generalized quantifiers and second order logics. Prace Nauk. Inst. Mat. Politech. Wrocław., 117–123. Cited on page 343.Google Scholar
Väänänen, J. 1991. A Cantor–Bendixson theorem for the space. Fundamenta Mathematicae, 137(3), 187–199. Cited on page 277.CrossRefGoogle Scholar
Väänänen, J. 1995. Games and trees in infinitary logic: A survey. Pages 105–138 of: Krynicki, M., Mostowski, M., and Szczerba, L. (eds), Quantifiers. Quad. Mat. Kluwer Academic Publishers. Cited on pages 276 and 277.Google Scholar
Väänänen (Ed.), J. 1999. Generalized quantifiers and computation. Lecture Notes in Computer Science, vol. 1754. Berlin: Springer-Verlag. Cited on page 343.CrossRefGoogle Scholar
Väänänen, J. 2007. Dependence Logic. London Mathematical Society Student Texts, vol. 70. Cambridge: Cambridge University Press. Cited on pages 205 and 208.CrossRefGoogle Scholar
Väänänen, J. 2008. How complicated can structures be? Nieuw Archief voor Wiskunde, June, 117–121. Cited on page 277.Google Scholar
Väänänen, J., and Veličković, B. 2004. Games played on partial isomorphisms. Archive für mathematische Logic, 43(1), 19–30. Cited on page 248.CrossRefGoogle Scholar
Väänänen, J., and Westerståhl, D. 2002. On the expressive power of monotone natural language quantifiers over finite models. Journal of Philosophical Logic, 31(4), 327–358. Cited on page 343.CrossRefGoogle Scholar
Väisänen, P. 2003. Almost free groups and long Ehrenfeucht–Fraïsségames. Annals of Pure and Applied Logic, 123(1–3), 101–134. Cited on page 277.CrossRefGoogle Scholar
van Benthem, J. 1984. Questions about quantifiers. Journal of Symbolic Logic, 49(2), 443–466. Cited on page 343.CrossRefGoogle Scholar
Vaught, R. 1964. The completeness of logic with the added quantifier “there are uncountably many”. Fundamenta Mathematicae, 54, 303–304. Cited on page 343.CrossRefGoogle Scholar
Vaught, R. 1973. Descriptive set theory in. Pages 574–598. Lecture Notes in Math., Vol. 337 of: Cambridge Summer School in Mathematical Logic (Cambridge, England, 1971). Berlin: Springer. Cited on pages 201, 209, 213, and 277.Google Scholar
Vaught, R. 1974. Model theory before 1945. Pages 153–172 of: Proceedings of the Tarski Symposium (Proceedings of Symposia in Pure Mathematics, Vol. XXV, Univ. California, Berkeley, Calif., 1971). Providence R.I.: Amer. Math. Soc. Cited on page 125.Google Scholar
von Neumann, J., and Morgenstern, O. 1944. Theory of Games and Economic Behavior. Princeton, New Jersey: Princeton University Press. Cited on page 28.Google Scholar
Walkoe, Wilbur John Jr. 1970. Finite partially-ordered quantification. Journal of Symbolic Logic, 35, 535–555. Cited on page 207.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Jouko Väänänen
  • Book: Models and Games
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511974885.012
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Jouko Väänänen
  • Book: Models and Games
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511974885.012
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Jouko Väänänen
  • Book: Models and Games
  • Online publication: 01 June 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511974885.012
Available formats
×