Skip to main content

About infinity, finiteness and finitization (in connection with the foundations of mathematics)

Part of the Lecture Notes in Mathematics book series (LNM,volume 873)

Keywords

  • Function Symbol
  • Formal Proof
  • Closed Formula
  • Finite Model
  • Induction Variable

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Shepherdson, J. C. Inner Models for Set Theory, J.S.L. v16 (1951) pp. 161–190, v17 (1952) pp. 225–237, v18 (1953) pp. 145–167.

    MathSciNet  MATH  Google Scholar 

  2. Yessenin-Volpin, A. S. Le programme ultra-intuitioniste des fondements des mathematiques, Infinitistic Methods, Warsawa (1961) pp. 201–223.

    Google Scholar 

  3. Yessenin-Volpin, A. S. The Ultra-intuitionistic Criticism and the Antitraditional Program for the Foundation of Mathematics, Intuitionism and Proof Theory, North Holland (1970) pp. 3–45.

    Google Scholar 

  4. Yessenin-Volpin, A. S. On the Ultraintuitionistic Justification of the Zermelo-Fraenkel System, I (in Russian), deposited with VINITI in 1969 and available from them in Xerox form (450 pp.).

    Google Scholar 

  5. Yessenin-Volpin, A. S. On the Main Problem in the Foundations of Mathematics, to appear in the Boston University Colloquium for the Philosophy of Science.

    Google Scholar 

  6. Kleene, S. C. Introduction to Metamathematics 1952, D. Van Nostrand Company, Inc., New York, Toronto, 550 pp.

    MATH  Google Scholar 

  7. Specker E. Dualität, Dialectica, 1958, 12, pp. 451–465.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Specker E. The Axiom of Choice in Quine's New Foundations for Mathematical Logic, Acad. USA, 1953, 39, pp. 972–975.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Quine, W.V.O. New Foundations for Mathematical Logic, Am, Math. Monthly, 1937, 44, pp. 70–80

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Jensen, Ronald Björn, On the consistency of a slight (?) modification of Quine's New Foundations, Synthese, 1968, 19, no. 1–2, pp. 250–263.

    CrossRef  MATH  Google Scholar 

  11. Yessenin-Volpin, A.S. On an Explanation of an Anti-traditional Paradox, 6th International Congress of Logic, Methodology and Philosophy of Science, Hannover, August 22–August 29, 1979, Abstracts [sec. 1, pp. 78–81].

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Yessenin-Volpin, A.S. (1981). About infinity, finiteness and finitization (in connection with the foundations of mathematics). In: Richman, F. (eds) Constructive Mathematics. Lecture Notes in Mathematics, vol 873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090740

Download citation

  • DOI: https://doi.org/10.1007/BFb0090740

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10850-4

  • Online ISBN: 978-3-540-38759-6

  • eBook Packages: Springer Book Archive