Definable forcing axiom: an alternative to Martin's axiom
نویسندگان
چکیده
منابع مشابه
The 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).
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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...
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In this paper we study the question assuming MA+¬CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalant to question of what is the additivity of Marczewski’s ideal s. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals. Introduction Let S be Sacks perfe...
متن کاملThe 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...
متن کاملThe Proper Forcing Axiom: a tutorial
In these notes we will present an exposition of the Proper Forcing Axiom (PFA). We will first discuss examples of the consequences of PFA. We will then present two proper partial orders which are used to force two combinatorial principles which follow from PFA: The P-Ideal Dichotomy (PID) and Todorcevic’s formulation of the Open Coloring Axiom. On one hand, these posets and the proofs of their ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1990
ISSN: 0166-8641
DOI: 10.1016/0166-8641(90)90112-f