Results 1 to 10 of about 275 (134)
Operations, climbability and the proper forcing axiom
Annals of Pure and Applied Logic, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yasuo Yoshinobu
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The proper forcing axiom and stationary set reflection [PDF]
Pacific Journal of Mathematics, 1991 Our main result is that the proper forcing axiom (PFA) is equiconsistent with ``PFA \(+\) there is a nonreflecting stationary subset of \(\omega_ 2''\).
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On the consistency strength of the proper forcing axiom
Advances in Mathematics, 2011 Recently the second author introduced combinatorial principles that characterize supercompactness for inaccessible cardinals but can also hold true for small cardinals. We prove that the proper forcing axiom PFA implies these principles hold for $ω_2$.
Matteo Viale
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The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis
Annals of Pure and Applied Logic, 2006 The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping Reflection Principle, a consequence of PFA.
Justin Tatch Moore
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The bounded proper forcing axiom and well orderings of the reals [PDF]
Mathematical Research Letters, 2006 We show that the bounded proper forcing axiom BPFA implies that there is a well-ordering of P(ω_1) which is Δ_1 definable with parameter a subset of ω_1. Our proof shows that if BPFA holds then any inner model of the universe of sets that correctly computes N_2 and also satisfies BPFA must contain all subsets of ω_1.
Boban Veličković
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Proper forcing axiom and selective separability
Topology and Its Applications, 2012 Selectively separable (or SS) spaces are becoming popular nowadays; perhaps less popular are SS\(^+\)-spaces which are those in which player II has a winning strategy for the following natural game: player I picks a dense set \(D_n\); player II picks a finite set \(E_n\subseteq D_n\). Player II wins if \(\bigcup_{n\in\omega}E_n\) is dense. In the paper
Alan Dow
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Internal forcing axioms: Martin's axiom and the proper forcing axiom
Bulletin of the Irish Mathematical Society, 1992 This introductory-expository paper contains the basic definitions as well as the most important first consequences of Martin's axiom as the generalization of the Baire category theorem, the non-existence of Luzin sets, results on \(Q\)-sets, non-existence of Suslin trees. The definition of the proper forcing axiom is also given.
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Journal of the Mathematical Society of Japan, 2017 Recently, David Aspero and Miguel Angel Mota discovered a new method of iterated forcing using models as side conditions. The side condition method with models was introduced by Stevo Todorcevic in the 1980s. The Aspero–Mota iteration enables us to force some $\Pi_2$-statements over $H(\aleph_2)$ with the continuum greater than $\aleph_2$.
Teruyuki Yorioka
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The bounded proper forcing axiom [PDF]
Journal of Symbolic Logic, 1995 AbstractThe 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 ∑1-reflecting, if for any regular cardinal χ, for all formulas φ, “H(χ) ⊨ ‘φ’” implies “∃δ < κ, H(δ) ⊨ ‘φ ...
Martin Goldstern, Saharon Shelah
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Strong homology and the proper forcing axiom [PDF]
Proceedings of the American Mathematical Society, 1989 This paper concerns applications of set theory to the problem of calculating the strong homology of certain subsets of Euclidean spaces. We prove the set theoretic result that it is consistent that every almost coinciding family indexed by
Dow, Alan +2 more
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