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We show that, like singular cardinals, and weakly compact cardinals, Jensen's core model K for measures of order zero  calculates correctly the successors of Jónsson cardinals, assuming
does not exist. Namely, if
is a Jónsson cardinal then
We show that Bounded Forcing Axioms (for instance, Martin's Axiom, the Bounded Proper Forcing Axiom, or the Bounded Martin's Maximum) are equivalent to principles of generic absoluteness, that is, they assert that if a
sentence of the language of set theory with parameters of small...
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