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Some consequences from Proper Forcing Axiom together with large continuum and the negation of Martin's Axiomopenaire
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), 2011 The Proper Forcing Axiom is a powerful extension of the Baire Category Theo- rem 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.
Justin Tatch Moore
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Distributive proper forcing axiom and cardinal invariants
Archive for Mathematical Logic, 2013In what follows, we assume the reader is familiar with all notions involved in the definitions of Martin's Axiom (\textbf{MA}) and the Proper Forcing Axiom (\textbf{PFA}) -- if this is not the case, see, respectively, [\textit{D. A. Martin} and \textit{R. M. Solovay}, Ann. Math. Logic 2, 143--178 (1970; Zbl 0222.02075)] and [\textit{J. E. Baumgartner},
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Generic Vopěnka’s Principle, remarkable cardinals, and the weak Proper Forcing Axiom
Archive for Mathematical Logic, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Joan Bagaria +2 more
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A fragment of Asperó–Mota’s finitely proper forcing axiom and entangled sets of reals
Fundamenta Mathematicae, 2020By a well-known result due to \textit{J. E. Baumgartner} [Fundam. Math. 79, 101--106 (1973; Zbl 0274.02037)], PFA implies that every two \(\aleph_1\)-dense sets of reals (without end points, by definition) are isomorphic. On the other hand, \textit{U. Avraham} and \textit{S. Shelah} [Isr. J. Math.
Teruyuki Yorioka
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Distributive proper forcing axiom and a left-right dichotomy of Cichoń’s diagram
Science China Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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