Ultraproducts and the axiom of choice

Norbert Brunner

Archivum Mathematicum (1986)

  • Volume: 022, Issue: 4, page 175-180
  • ISSN: 0044-8753

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Brunner, Norbert. "Ultraproducts and the axiom of choice." Archivum Mathematicum 022.4 (1986): 175-180. <http://eudml.org/doc/18193>.

@article{Brunner1986,
author = {Brunner, Norbert},
journal = {Archivum Mathematicum},
keywords = {Dedekind-finite; axiom of choice; amorphous set; topology of the reals; ultraproduct; permutation model; Rubin's axiom; -spaces; ZF- models without full AC},
language = {eng},
number = {4},
pages = {175-180},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Ultraproducts and the axiom of choice},
url = {http://eudml.org/doc/18193},
volume = {022},
year = {1986},
}

TY - JOUR
AU - Brunner, Norbert
TI - Ultraproducts and the axiom of choice
JO - Archivum Mathematicum
PY - 1986
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 022
IS - 4
SP - 175
EP - 180
LA - eng
KW - Dedekind-finite; axiom of choice; amorphous set; topology of the reals; ultraproduct; permutation model; Rubin's axiom; -spaces; ZF- models without full AC
UR - http://eudml.org/doc/18193
ER -

References

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  1. A. Blass, A model without ultrafilters, Bull. Acad. Polon. 25 (1977), 329-331. (1977) Zbl0365.02054MR0476510
  2. N. Brunner, Lindelöf-Räume und Auswahlaxiom, Anzeiger Akad. Wiss. Wien 119 (1982), 161-165. (1982) MR0728812
  3. N. Brunner, Hilberträume mit amorphen Basen, Compositio Math. 52 (1984) 381-387. (1984) Zbl0554.47001MR0756729
  4. J. D. Halpern, On a question of Tarski and a theorem of Kurepa, Pacific J. Math. 41 (1972), 111-121. (1972) MR0307912
  5. J. L. Hickman, Groups in models of set theory, Bull. Australian Math. Soc. 14 (1976), 199-232. (1976) Zbl0324.02055MR0409178
  6. P. E. Howard, Loš theorem and the BPI imply AC, Proc. A.M.S. 49 (1975), 426-428. (1975) MR0384548
  7. T. Jech, The Axiom of Choice, New York 1973. (1973) Zbl0259.02052MR0396271
  8. A. Levy, Axioms of Multiple Choice, Fundamenta Math. 59 (1962), 475-483. (1962) Zbl0134.24805MR0139528
  9. G. P. Monro, Generic Extensions without AC, J. Symbolic Logic 48 (1983), 39-52. (1983) MR0693246
  10. D. Pincus, Strength of the Hahn Banach Theorem, in Victoria Symp. Nonstandard Analysis, Springer LN 369 (1972). (1972) MR0476512
  11. H. Rubin J. E. Rubin, Equivalents of AC II, North Holland P.C. (1985). (1985) 

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