Woodin's Axiom ( * ), Bounded Forcing Axioms, and Precipitous Ideals on Ω 1
نویسندگان
چکیده
If the Bounded Proper Forcing Axiom BPFA holds, then Mouse Reflection holds at א2 with respect to all mouse operators up to the level of Woodin cardinals in the next ZFC–model. This yields that if Woodin’s Pmax axiom (∗) holds, then BPFA implies that V is closed under the “Woodin-in-the-nextZFC–model” operator. We also discuss stronger Mouse Reflection principles which we show to follow from strengthenings of BPFA, and we discuss the theory BPFA plus “NSω1 is precipitous” and strengthenings thereof. Along the way, we answer a question of Baumgartner and Taylor, [2, Question 6.11].
منابع مشابه
Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on ω₁
If the Bounded Proper Forcing Axiom BPFA holds, then Mouse Reflection holds at א2 with respect to all mouse operators up to the level of Woodin cardinals in the next ZFC–model. This yields that if Woodin’s Pmax axiom (∗) holds, then BPFA implies that V is closed under the “Woodin-in-the-nextZFC–model” operator. We also discuss stronger Mouse Reflection principles which we show to follow from st...
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