The bounded proper forcing axiom
نویسندگان
چکیده
منابع مشابه
The Bounded Proper Forcing Axiom
The bounded proper forcing axiom BPFA is the statement that for any family of א1 many maximal antichains of a proper forcing notion, each of size א1, there is a directed set meeting all these antichains. A regular cardinal κ is called Σ1-reflecting, if for any regular cardinal χ, for all formulas φ, “H(χ) |= ‘φ’ ” implies “∃δ<κ, H(δ) |= ‘φ’ ” We show that BPFA is equivalent to the statement tha...
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The Proper Forcing Axiom is a powerful extension of the Baire Category Theorem which has proved highly effective in settling mathematical statements which are independent of ZFC. In contrast to the Continuum Hypothesis, it eliminates a large number of the pathological constructions which can be carried out using additional axioms of set theory. Mathematics Subject Classification (2000). Primary...
متن کاملBounded Proper Forcing Axiom and Well Orderings of the Reals
We show that the bounded proper forcing axiom BPFA implies that there is a well-ordering of P(ω1) which is ∆1 definable with parameter a subset of ω1. Our proof shows that if BPFA holds then any inner model of the universe of sets that correctly computes א2 and also satisfies BPFA must contain all subsets of ω1. We show as applications how to build minimal models of BPFA and that BPFA implies t...
متن کاملThe Bounded Axiom A Forcing Axiom
We introduce the Bounded Axiom A Forcing Axiom(BAAFA). It turns out that it is equiconsistent with the existence of a regular Σ2-correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom(BPFA).
متن کاملBounded Martin’s Maximum is stronger than the Bounded Semi-proper Forcing Axiom
We show that if Bounded Martin’s Maximum (BMM) holds then for every X ∈ V there is an inner model with a strong cardinal containing X. In particular, by [1], BMM is strictly stronger consistency-wise than the Bounded Semi-Proper Forcing Axiom (BSPFA).
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 1995
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2275509