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Potent axioms

Published:1986 Issue:1 Volume:294 Page:1-28
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Foreman Matthew

Abstract

This paper suggests alternatives to the ordinary large cardinal axioms of set theory. These axioms can be viewed as generalizations of large cardinals and exhibit many of the same phenomena. They are shown to imply the G.C.H., every set of reals in L ( R ) L({\mathbf {R}}) is Lebesgue measurable, and various results in combinatorics, algebra and model theory.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1986-294-01/S0002-9947-1986-0819932-2/S0002-9947-1986-0819932-2.pdf

Reference27 articles.

1. Generic graph construction;Baumgartner, James E.;J. Symbolic Logic,1984

2. Saturation properties of ideals in generic extensions. I;Baumgartner, James E.;Trans. Amer. Math. Soc.,1982

3. More saturated ideals;Foreman, Matthew,1983

4. Large cardinals and strong model theoretic transfer properties;Foreman, Matthew;Trans. Amer. Math. Soc.,1982

5. M. Foreman and R. Laver, A graph transfer property (to appear).

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