Independence of the prime ideal theorem from the Hahn Banach theorem
Author:
David Pincus
Journal:
Bull. Amer. Math. Soc. 78 (1972), 766770
MSC (1970):
Primary 02K05; Secondary 46A05
MathSciNet review:
0297565
Fulltext PDF
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 (English, with Russian summary). MR 0282186
(43 #7899)
 2.
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
(44 #1557)
 3.
W.
A. J. Luxemburg, Two applications of the method of
construction by ultrapowers to anaylsis, Bull.
Amer. Math. Soc. 68
(1962), 416–419. MR 0140417
(25 #3837), http://dx.doi.org/10.1090/S000299041962108246
 4.
W.
A. J. Luxemburg, Reduced powers of the real number system and
equivalents of the HahnBanach 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
(38 #5616)
 5.
Andrzej
Mostowski, Axiom of choice for finite sets, Fund. Math.
33 (1945), 137–168. MR 0016352
(8,3q)
 6.
David
Pincus, Support structures for the axiom of choice, J.
Symbolic Logic 36 (1971), 28–38. MR 0282827
(44 #61)
 7.
J.
Łoś and C.
RyllNardzewski, On the application of Tychonoff’s theorem in
mathematical proofs, Fund. Math. 38 (1951),
233–237. MR 0048795
(14,70h)
 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), 191194. 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. 83134. MR 284328
 3.
 W. A. J. Luxemburg, Two applications of the method of construction by ultrapowers to analysis, Bull. Amer. Math. Soc. 68 (1962), 416419. 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), 137168. MR 8, 3. MR 16352
 6.
 D. Pincus, Support structures for the axiom of choice, J. Symbolic Logic 36 (1971), 2838. MR 282827
 7.
 J. Łoś and C. RyllNardzewski, On the applications of Tychonoff's theorem in mathematical proofs, Fund Math. 38 (1951), 233237. MR 14, 70. MR 48795
Similar Articles
Retrieve articles in Bulletin of the American Mathematical Society
with MSC (1970):
02K05,
46A05
Retrieve articles in all journals
with MSC (1970):
02K05,
46A05
Additional Information
DOI:
http://dx.doi.org/10.1090/S000299041972130258
PII:
S 00029904(1972)130258
