Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  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.

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References
References
Beklemishev, L.D. [1995] Iterated local reflection versus iterated consistency. Annals of Pure and Applied Logic, 75 Google Scholar, 25–48.
Beklemishev, L.D. [1997] Notes on local reflection principles. Theoria, 58 Google Scholar, 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 Google Scholar 1983.
Browder, F.E. (ed.) [1976 Google Scholar] 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 Google Scholar, pp. 35–92.
Feferman, S. [1962] Transfinite recursive progressions of axiomatic theories. The Journal of Symbolic Logic, Volume 27 Google Scholar, Number 3, 259–316.
Feferman, S. [1984] Kurt Gödel: Conviction and Caution. Philosophia Naturalis (1984), 21 Google Scholar(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 Google Scholar, 1993.
Feferman, S. et al., editors, Kurt Gödel: Collected Works. Vol III, Oxford Google Scholar 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 Google Scholar: Kluwer Academic.
Feferman, S. and Spector, C. [1962] Incompleteness along paths in progressions of theories. The Journal of Symbolic Logic, Volume 27 Google Scholar, Number 4, 383–390.
Franzén, T. [1987] Provability and Truth. Acta universitatis stockholmiensis, Stockholm Studies in Philosophy 9. Stockholm Google Scholar: Almqvist & Wiksell International.
Hájek, P. and Pudlák, P. [1993] Metamathematics of First Order Arithmetic. Berlin Google Scholar: New York: Springer-Verlag.
Hardy, G.H. [1929] Mathematical Proof, Mind, Vol. XXXVIII Google Scholar, No. 149.
Harrison, J. [1995] Metatheory and Reflection in Theorem Proving: A Survey and Critique. Technical Report CRC-053, SRI Cambridge Google Scholar.
Pudlák, P. [1999] A note on applicability of the completeness theorem to human mind, Annals of Pure and Applied Logic 96 Google Scholar, pp. 335–342
Quine, V.W.O. [1969] Set Theory and Its Logic Google Scholar. 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 Google Scholar.
Shoenfield, J. [1967] Mathematical Logic, Addison-Wesley, Reading, MA Google Scholar. Second edition, A K Peters, 2001.
Simpson, S.G. [1999] Subsystems of Second Order Analysis Google Scholar. Perspectives in Mathematical Logic, Springer-Verlag.
Smorynski, C. [1977] The Incompleteness Theorems. In: Barwise, J. (editor): Handbook of Mathematical Logic, North-Holland, Amsterdam Google Scholar.
Smullyan, R.M. [1992] Recursion Theory for Metamathematics. New York Google Scholar: Oxford University Press.
Smullyan, R.M. [1993] Gödel's incompleteness theorems. New York Google Scholar: Oxford University Press.
Tarski, A. [1944] The Semantic Conception of Truth and the Foundations of Semantics. Philosophy and Phenomenological Research 4 Google Scholar.
Zermelo, E. [1908] Investigations in the foundations of set theory I. Translation in From Frege to Gödel, van, Heijenoort Google Scholar (editor), Harvard University Press, 1971.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 1965 *
Loading metrics...

Book summary page views

Total views: 3613 *
Loading metrics...

* Views captured on Cambridge Core between 30th March 2017 - 4th April 2025. This data will be updated every 24 hours.

Usage data cannot currently be displayed.