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  1. A microscopic approach to Souslin-tree constructions, Part I.Ari Meir Brodsky & Assaf Rinot - 2017 - Annals of Pure and Applied Logic 168 (11):1949-2007.
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  • Stacking mice.Ronald Jensen, Ernest Schimmerling, Ralf Schindler & John Steel - 2009 - Journal of Symbolic Logic 74 (1):315-335.
    We show that either of the following hypotheses imply that there is an inner model with a proper class of strong cardinals and a proper class of Woodin cardinals. 1) There is a countably closed cardinal k ≥ N₃ such that □k and □(k) fail. 2) There is a cardinal k such that k is weakly compact in the generic extension by Col(k, k⁺). Of special interest is 1) with k = N₃ since it follows from PFA by theorems of (...)
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  • Some results about (+) proved by iterated forcing.Tetsuya Ishiu & Paul B. Larson - 2012 - Journal of Symbolic Logic 77 (2):515-531.
    We shall show the consistency of CH+ᄀ(+) and CH+(+)+ there are no club guessing sequences on ω₁. We shall also prove that ◊⁺ does not imply the existence of a strong club guessing sequence ω₁.
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  • Club guessing sequences and filters.Tetsuya Ishiu - 2005 - Journal of Symbolic Logic 70 (4):1037-1071.
    We investigate club guessing sequences and filters. We prove that assuming V=L, there exists a strong club guessing sequence on μ if and only if μ is not ineffable for every uncountable regular cardinal μ. We also prove that for every uncountable regular cardinal μ, relative to the existence of a Woodin cardinal above μ, it is consistent that every tail club guessing ideal on μ is precipitous.
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  • Chain conditions of products, and weakly compact cardinals.Assaf Rinot - 2014 - Bulletin of Symbolic Logic 20 (3):293-314,.
    The history of productivity of the κ-chain condition in partial orders, topological spaces, or Boolean algebras is surveyed, and its connection to the set-theoretic notion of a weakly compact cardinal is highlighted. Then, it is proved that for every regular cardinal κ > א1, the principle □ is equivalent to the existence of a certain strong coloring c : [κ]2 → κ for which the family of fibers T is a nonspecial κ-Aronszajn tree. The theorem follows from an analysis of (...)
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  • The Club Guessing Ideal: Commentary on a Theorem of Gitik and Shelah.Matthew Foreman & Peter Komjath - 2005 - Journal of Mathematical Logic 5 (1):99-147.
    It is shown in this paper that it is consistent (relative to almost huge cardinals) for various club guessing ideals to be saturated.
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  • Trees, subtrees and order types.Stevo B. Todorčević - 1981 - Annals of Mathematical Logic 20 (3):233.
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  • The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
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  • The combinatorial principle ⋄#.Keith J. Devlin - 1982 - Journal of Symbolic Logic 47 (4):888-899.
    We consider various strengthenings of the combinatorial principle ⋄ + which are provable from V = L, and give applications in set theory.
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