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References

Published online by Cambridge University Press:  30 March 2017

Torkel Franzén
Affiliation:
Luleå Tekniska Universitet, Sweden
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Inexhaustibility
A Non-Exhaustive Treatment
, pp. 293 - 296
Publisher: Cambridge University Press
Print publication year: 2004

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References

Beklemishev, L.D. [1995] Iterated local reflection versus iterated consistency. Annals of Pure and Applied Logic, 75, 25–48.Google Scholar
Beklemishev, L.D. [1997] Notes on local reflection principles. Theoria, 58, part 3, 139–146.Google Scholar
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.Google Scholar
Feferman, S. [1962] Transfinite recursive progressions of axiomatic theories. The Journal of Symbolic Logic, Volume 27, Number 3, 259–316.Google Scholar
Feferman, S. [1984] Kurt Gödel: Conviction and Caution. Philosophia Naturalis (1984), 21(2–4):546–562.Google Scholar
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.Google Scholar
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.Google Scholar
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. 335–342Google Scholar
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.Google Scholar
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  • References
  • Torkel Franzén, Luleå Tekniska Universitet, Sweden
  • Book: Inexhaustibility
  • Online publication: 30 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316755969.017
Available formats
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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
  • Torkel Franzén, Luleå Tekniska Universitet, Sweden
  • Book: Inexhaustibility
  • Online publication: 30 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316755969.017
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
  • Torkel Franzén, Luleå Tekniska Universitet, Sweden
  • Book: Inexhaustibility
  • Online publication: 30 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316755969.017
Available formats
×