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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Potent axioms


Author: Matthew Foreman
Journal: Trans. Amer. Math. Soc. 294 (1986), 1-28
MSC: Primary 03E65; Secondary 03E15, 03E50, 03E55, 04A30
DOI: https://doi.org/10.1090/S0002-9947-1986-0819932-2
MathSciNet review: 819932
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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({\mathbf{R}})$ is Lebesgue measurable, and various results in combinatorics, algebra and model theory.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0819932-2
Article copyright: © Copyright 1986 American Mathematical Society