Potent axioms

Foreman, Matthew

doi:10.1090/S0002-9947-1986-0819932-2

Potent axioms
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by Matthew Foreman

Trans. Amer. Math. Soc. 294 (1986), 1-28

DOI: https://doi.org/10.1090/S0002-9947-1986-0819932-2

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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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