Independence of the prime ideal theorem from the Hahn Banach theorem

Author:
David Pincus

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

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References | Similar Articles | Additional Information

**1.**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. MR**282186****2.**J. D. Halpern and A. Levy,*The Boolean prime ideal does not imply the axiom of choice*, Proc. Sympos. Pure Math., vol. 18, part 1, Amer. Math. Soc., Providence, R.I., 1970, pp. 83-134. MR**284328****3.**W. A. J. Luxemburg,*Two applications of the method of construction by ultrapowers to analysis*, Bull. Amer. Math. Soc. 68 (1962), 416-419. MR 25 #3837. MR**140417****4.**W. A. J. Luxemburg,*Reduced powers of the real number system and equivalents of the Hahn Banach extension theorem*, Internat. Sympos. on Applications of Model Theory to Algebraic Analysis, and Probability, Holt, Rinehart and Winston, New York, 1969. MR**237327****5.**A. Mostowski,*Axion of choice for finite sets*, Fund. Math. 33 (1945), 137-168. MR 8, 3. MR**16352****6.**D. Pincus,*Support structures for the axiom of choice*, J. Symbolic Logic 36 (1971), 28-38. MR**282827****7.**J. Łoś and C. Ryll-Nardzewski,*On the applications of Tychonoff's theorem in mathematical proofs*, Fund Math. 38 (1951), 233-237. MR 14, 70. MR**48795**

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DOI:
https://doi.org/10.1090/S0002-9904-1972-13025-8