Skip to main content
SpringerLink
Log in

The strength of the Hahn-Banach theorem

  • Conference paper
  • First Online:
Book cover Victoria Symposium on Nonstandard Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 369))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. J. L. Bell and D. H. Fremlen, A geometric form of the axiom of choice, Fund. Math. (1972), to appear.

    Google Scholar 

  2. P. J. Cohen, Independence of the axiom of choice, mimeographed notes, Stanford University.

    Google Scholar 

  3. P. J. Cohen, Set Theory and the Continuum Hypothesis, Benjamin, 1966

    Google Scholar 

  4. M. M. Day, Normed Linear Spaces, Springer, 1962.

    Google Scholar 

  5. S. Fefferman, Some applications of the notions of forcing and generic set, Fund. Math. 56 (1965), pp. 325–345.

    MathSciNet  Google Scholar 

  6. J. D. Halpern and H. Lauchli, A partition theorem, Trans. A.M.S. 124 (1966), pp. 360–367.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. D. Halpern and A. Levy, the Boolean prime ideal theorem does not imply the axiom of choice, Proc. Symp. Pure Math. Vol. XIII Part I, pp. 83–134.

    Google Scholar 

  8. T. Jech and A. Sochor, Applications of the ϑ model, Bull. Acad. Polon. Ser. Sec. 14 (1966), pp. 351–355.

    MathSciNet  MATH  Google Scholar 

  9. J. Los and C. Ryll-Nardzewski, Effectiveness of the representation theory for Boolean algebras, Fund. Math. 41 (1954), pp. 49–56.

    MathSciNet  MATH  Google Scholar 

  10. J. Los and C. Ryll-Nardzewski, On the applications of Tychanov’s theorem in mathematical proofs, Fund. Math. 38 (1951), pp. 233–237.

    MathSciNet  MATH  Google Scholar 

  11. W. A. J. Luxemburg, 2 applications of the method of construction by ultrapowers to analysis, Bull. A.M.S. 68 (1962), pp. 416–419.

    Article  MathSciNet  MATH  Google Scholar 

  12. W. A. J. Luxemburg, Reduced powers of the real number system and equivalents of the Hahn-Banach extension theorem, Int. Sympos on the Application of Model Theory to Alg. Anal. and Probability, Holt, Rinehart and Winston 1969.

    Google Scholar 

  13. J. Mycielski, Two Remarks on Tychonoff’s Product Theorem, Bull. Akad. Polon. Ser. Sci. 12 (1964), pp. 439–441.

    MathSciNet  MATH  Google Scholar 

  14. D. Pincus, Support structures for the axiom of choice, J.S.L. 35 (1971), pp. 28–38.

    MathSciNet  MATH  Google Scholar 

  15. D. Pincus, Zermelo Fraenkel consistency results by Fraenkel Mostowski Methods J.S.L. (to appear).

    Google Scholar 

  16. D. Pincus, Nonperfect sets, Baire diagonal sets, and well ordering the continuum. Submitted for publication.

    Google Scholar 

  17. D. Pincus, Independence of the Prime Ideal theorem from the Hahn Banach Theorem Bull. A.M.S. 78 (1972), to appear.

    Google Scholar 

  18. J. R. Shoenfield, Mathematical Logic, Addision Wesley (1967).

    Google Scholar 

  19. J. R. Shoenfield, Unramified Forcing, Proc. Symp. Pure Math. XIII Vol. I, pp. 357–381.

    Google Scholar 

  20. R. M. Solovay, A model of set theory in which every set of reals is Lesbague measurable Ann. of Math. 92 (1970), pp. 1–58.

    Article  MathSciNet  MATH  Google Scholar 

  21. W. Sierpinski, Sur un probleme conduisant a un ensemble non measurable, Fund. Math. 10 (1927), pp. 177–179.

    MATH  Google Scholar 

  22. W. Sierpinski, Functions additives non completement additives et functions non measurables, Fund. Math. 30 (1938), pp. 96–99.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Seattle, Wash.

    David Pincus

Authors
  1. David Pincus
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Albert Hurd Peter Loeb

Rights and permissions

Reprints and permissions

Copyright information

© 1974 Springer-Verlag

About this paper

Cite this paper

Pincus, D. (1974). The strength of the Hahn-Banach theorem. In: Hurd, A., Loeb, P. (eds) Victoria Symposium on Nonstandard Analysis. Lecture Notes in Mathematics, vol 369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066014

Download citation

  • DOI: https://doi.org/10.1007/BFb0066014

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06656-9

  • Online ISBN: 978-3-540-37928-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation