Independence of the prime ideal theorem from the Hahn Banach theorem
HTML articles powered by AMS MathViewer
- by David Pincus PDF
- Bull. Amer. Math. Soc. 78 (1972), 766-770
References
- J. L. Bell and F. Jellett, On the relationship between the Boolean prime ideal theorem and two principles in functional analysis, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 191–194 (English, with Russian summary). MR 282186
- J. D. Halpern and A. Lévy, The Boolean prime ideal theorem does not imply the axiom of choice. , Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 83–134. MR 0284328
- W. A. J. Luxemburg, Two applications of the method of construction by ultrapowers to anaylsis, Bull. Amer. Math. Soc. 68 (1962), 416–419. MR 140417, DOI 10.1090/S0002-9904-1962-10824-6
- W. A. J. Luxemburg, Reduced powers of the real number system and equivalents of the Hahn-Banach extension theorem, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 123–137. MR 0237327
- Andrzej Mostowski, Axiom of choice for finite sets, Fund. Math. 33 (1945), 137–168. MR 16352, DOI 10.4064/fm-33-1-137-168
- David Pincus, Support structures for the axiom of choice, J. Symbolic Logic 36 (1971), 28–38. MR 282827, DOI 10.2307/2271513
- J. Łoś and C. Ryll-Nardzewski, On the application of Tychonoff’s theorem in mathematical proofs, Fund. Math. 38 (1951), 233–237. MR 48795, DOI 10.4064/fm-38-1-233-237
Additional Information
- Journal: Bull. Amer. Math. Soc. 78 (1972), 766-770
- MSC (1970): Primary 02K05; Secondary 46A05
- DOI: https://doi.org/10.1090/S0002-9904-1972-13025-8
- MathSciNet review: 0297565