In set theory, a branch of mathematical logic, Martin's maximum, introduced by and named after Donald Martin, is a generalization of the proper forcing axiom, itself a generalization of Martin's axiom. It represents the broadest class of forcings for which a forcing axiom is consistent. The existence of a supercompact cardinal implies the consistency of Martin's maximum. The proof uses Shelah's theories of semiproper forcing and iteration with revised countable supports.
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