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Transactions of the American Mathematical Society

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Potent axioms

Author: Matthew Foreman
Journal: Trans. Amer. Math. Soc. 294 (1986), 1-28
MSC: Primary 03E65; Secondary 03E15, 03E50, 03E55, 04A30
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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Article copyright: © Copyright 1986 American Mathematical Society

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