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  1. Home
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  3. Inexhaustibility
  • Cited by 1
Publisher:
Cambridge University Press
Online publication date:
March 2017
Print publication year:
2004
Online ISBN:
9781316755969
DOI:
https://doi.org/10.1017/9781316755969
Subjects:
Mathematics, Logic, Categories and Sets, Logic, Philosophy, Programming Languages and Applied Logic
Series:
Lecture Notes in Logic (16)
Information

Book description

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel's incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.

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Contents

Contents
References
References
Beklemishev, L.D. [1995] Iterated local reflection versus iterated consistency. Annals of Pure and Applied Logic, 75, 25–48.
Beklemishev, L.D. [1997] Notes on local reflection principles. Theoria, 58, part 3, 139–146.
Bernays, P. [1935] On Platonism in Mathematics, in P., Benacerraf and H., Putnam (editors), Philosophy of Mathematics: Selected Readings, 2nd ed. Cambridge 1983.
Browder, F.E. (ed.) [1976] Mathematical Developments Arising from Hilbert Problems, number 28 in American Mathematical Society: Proceedings of Symposia in Pure Mathematics.
Feferman, S. [1960] Arithmetization of metamathematics in a general setting. Fundamenta Mathematicae, vol. 49, pp. 35–92.
Feferman, S. [1962] Transfinite recursive progressions of axiomatic theories. The Journal of Symbolic Logic, Volume 27, Number 3, 259–316.
Feferman, S. [1984] Kurt Gödel: Conviction and Caution. Philosophia Naturalis (1984), 21(2–4):546–562.
Feferman, S. [1993] What rests on what? The proof-theoretic analysis of mathematics, in Philosophy of Mathematics, Part I, pp. 147–171, Proceedings of the 15th International Wittgenstein Symposium, Verlag Hölder-Pichler-Tempsky, Vienna, 1993.
Feferman, S. et al., editors, Kurt Gödel: Collected Works. Vol III, Oxford 1995.
Feferman, S. and Hellman, G. [1999] Challenges to Predicative Foundations of Arithmetic, in Gila, Sher and Richard L., Tieszen, editors, Between Logic and Intuition: Essays in Honor of Charles Parsons, pp. 317–339. Dordrecht & Boston: Kluwer Academic.
Feferman, S. and Spector, C. [1962] Incompleteness along paths in progressions of theories. The Journal of Symbolic Logic, Volume 27, Number 4, 383–390.
Franzén, T. [1987] Provability and Truth. Acta universitatis stockholmiensis, Stockholm Studies in Philosophy 9. Stockholm: Almqvist & Wiksell International.
Hájek, P. and Pudlák, P. [1993] Metamathematics of First Order Arithmetic. Berlin: New York: Springer-Verlag.
Hardy, G.H. [1929] Mathematical Proof, Mind, Vol. XXXVIII, No. 149.
Harrison, J. [1995] Metatheory and Reflection in Theorem Proving: A Survey and Critique. Technical Report CRC-053, SRI Cambridge.
Pudlák, P. [1999] A note on applicability of the completeness theorem to human mind, Annals of Pure and Applied Logic 96, pp. 335–342
Quine, V.W.O. [1969] Set Theory and Its Logic. Second edition, Harvard University Press.
Schmerl, U.R. [1979] A fine structure generated by reflection formulas over Primitive Recursive Arithmetic, in M., Boffa, D., van Dalen and K., McAloon, editors, Logic Colloquium ‘78, North Holland, Amsterdam.
Shoenfield, J. [1967] Mathematical Logic, Addison-Wesley, Reading, MA. Second edition, A K Peters, 2001.
Simpson, S.G. [1999] Subsystems of Second Order Analysis. Perspectives in Mathematical Logic, Springer-Verlag.
Smorynski, C. [1977] The Incompleteness Theorems. In: Barwise, J. (editor): Handbook of Mathematical Logic, North-Holland, Amsterdam.
Smullyan, R.M. [1992] Recursion Theory for Metamathematics. New York: Oxford University Press.
Smullyan, R.M. [1993] Gödel's incompleteness theorems. New York: Oxford University Press.
Tarski, A. [1944] The Semantic Conception of Truth and the Foundations of Semantics. Philosophy and Phenomenological Research 4.
Zermelo, E. [1908] Investigations in the foundations of set theory I. Translation in From Frege to Gödel, van, Heijenoort (editor), Harvard University Press, 1971.

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