Forcing axioms and projective sets of reals
This paper is an introduction to forcing axioms and large cardinals. Specifically, we shall discuss the large cardinal strength of forcing axioms in the presence of regularity properties for projective sets of reals. The new result shown in this paper says that ZFC + the bounded proper forcing axiom (BPFA) + “every projective set of reals is Lebesgue measurable” is equiconsistent with ZFC + “there is a Σ1 reflecting cardinal above a remarkable cardinal.”
KeywordsOrder Type Inaccessible Cardinal Maximal Antichains Singular Cardinal Supercompact Cardinal
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