Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Martin's axiom and saturated models


Authors: Erik Ellentuck and R. v. B. Rucker
Journal: Proc. Amer. Math. Soc. 34 (1972), 243-249
MSC: Primary 02K05
DOI: https://doi.org/10.1090/S0002-9939-1972-0290960-7
MathSciNet review: 0290960
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: $ {2^{{\aleph _0}}} > {\aleph _1}$ is consistent with the existence of an ultrafilter F on $ \omega $ such that for every countable structure $ \mathfrak{A}$ the ultrapower $ {\mathfrak{A}^\omega }/F$ is saturated.


References [Enhancements On Off] (What's this?)

  • [1] H. J. Keisler, Ultraproducts and saturated models, Nederl. Akad. Wetensch. Proc. Ser. A 67=Indag. Math. 26 (1964), 178-186. MR 29 #5745. MR 0168483 (29:5745)
  • [2] K. Kunen, Ultrafilters and independent sets (to appear). MR 0314619 (47:3170)
  • [3] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143-178. MR 42 #5787. MR 0270904 (42:5787)
  • [4] M. Morely and R. Vaught, Homogeneous universal models, Math. Scand. 11 (1962), 37-57. MR 27 #37. MR 0150032 (27:37)
  • [5] D. Scott and R. M. Solovay, Boolean valued model of set theory, Proc. Sympos. Pure Math., vol. 13, part II, Amer. Math. Soc., Providence, R.I. (to appear).
  • [6] R. M. Solovay and S. Tennenbaum, Iterated Cohen extensions and Souslin's problem, Ann. of Math. 94 (1971), 201-245. MR 0294139 (45:3212)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02K05

Retrieve articles in all journals with MSC: 02K05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0290960-7
Keywords: Saturation, ultraproduct, Martin's axiom
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society