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  1. Rado’s Conjecture and its Baire version.Jing Zhang - 2019 - Journal of Mathematical Logic 20 (1):1950015.
    Rado’s Conjecture is a compactness/reflection principle that says any nonspecial tree of height ω1 has a nonspecial subtree of size ℵ1. Though incompatible with Martin’s Axiom, Rado’s Conjecture turns out to have many interesting consequences that are also implied by certain forcing axioms. In this paper, we obtain consistency results concerning Rado’s Conjecture and its Baire version. In particular, we show that a fragment of PFA, which is the forcing axiom for Baire Indestructibly Proper forcings, is compatible with the Baire (...)
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  • Bounded dagger principles.Toshimichi Usuba - 2014 - Mathematical Logic Quarterly 60 (4-5):266-272.
    For an uncountable cardinal κ, let be the assertion that every ω1‐stationary preserving poset of size is semiproper. We prove that is a strong principle which implies a strong form of Chang's conjecture. We also show that implies that is presaturated.
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  • Combinatorial dichotomies in set theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.
    We give an overview of a research line concentrated on finding to which extent compactness fails at the level of first uncountable cardinal and to which extent it could be recovered on some other perhaps not so large cardinal. While this is of great interest to set theorists, one of the main motivations behind this line of research is in its applicability to other areas of mathematics. We give some details about this and we expose some possible directions for further (...)
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