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weak diamond Forcing Axioms Local Club Condensation. Erdos-Hajnal graphs stick Microscopic Approach Distributive tree Dowker space Kurepa Hypothesis Amenable C-sequence Knaster and friends polarized partition relation incompactness Generalized descriptive set theory Shelah's Strong Hypothesis Subtle tree property Commutative projection system square principles free Souslin tree Ulam matrix SNR Large Cardinals Whitehead Problem Sigma-Prikry Singular cardinals combinatorics OCA diamond star middle diamond Almost Souslin Diamond-sharp reflection principles Nonspecial tree Hereditarily Lindelöf space Almost-disjoint family square Vanishing levels Partition relations for trees AIM forcing Respecting tree xbox positive partition relation Precaliber Erdos Cardinal higher Baire space Commutative cancellative semigroups Subadditive Reflecting stationary set Mandelbrot set Ineffable cardinal Weakly compact cardinal stationary hitting Filter reflection Luzin set sap Minimal Walks Dushnik-Miller tensor product graph Countryman line free Boolean algebra Coherent tree weak Kurepa tree Forcing Monotonically far Uniformly coherent Strongly compact cardinal full tree Successor of Singular Cardinal Aronszajn tree Diamond ccc Well-behaved magma GMA Prikry-type forcing Hindman's Theorem Cardinal function Fast club Entangled linear order HOD Singular cofinality Uniformization Interval topology on trees stationary reflection Antichain PFA(S)[S] Open Access 54G20 Strong coloring Club Guessing Small forcing Postprocessing function O-space Cardinal Invariants Absoluteness Rado's conjecture Lipschitz reduction Singular Density Subtle cardinal Slim tree Poset transformations approachability ideal Foundations Knaster projective Boolean algebra Martin's Axiom Uniformly homogeneous Non-saturation Fodor-type reflection Partition Relations Ascending path Hedetniemi's conjecture Universal Sequences Diamond for trees L-space coloring number unbounded function Generalized Clubs P-Ideal Dichotomy Selective Ultrafilter Successor of Regular Cardinal weak square Cohen real Strongly Luzin set Constructible Universe Subnormal ideal strongly bounded groups PFA Sakurai's Bell inequality Axiom R Intersection model Parameterized proxy principle ZFC construction Sierpinski's onto mapping principle Was Ulam right? S-Space Analytic sets Forcing with side conditions C-sequence indecomposable filter super-Souslin tree Ascent Path Square-Brackets Partition Relations Chromatic number b-scale Rainbow sets Rock n' Roll Closed coloring very good scale nonmeager set Fat stationary set Ostaszewski square club_AD Chang's conjecture perfectly normal Souslin Tree Ramsey theory over partitions specializable Souslin tree Jonsson cardinal Almost countably chromatic Reduced Power regressive Souslin tree Prevalent singular cardinals Iterated forcing countably metacompact Greatly Mahlo
Tag Archives: Generalized Clubs
The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … Continue reading
On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
