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Fast club C-sequence Rainbow sets Subtle cardinal Knaster and friends Singular cofinality Hindman's Theorem Non-saturation Countryman line Forcing with side conditions Strongly Luzin set Cardinal Invariants Rado's conjecture Amenable C-sequence specializable Souslin tree Reflecting stationary set Kurepa Hypothesis Ineffable cardinal Open Access Axiom R Luzin set AIM forcing Erdos-Hajnal graphs free Boolean algebra Intersection model Almost countably chromatic projective Boolean algebra Ulam matrix transformations Sakurai's Bell inequality GMA Aronszajn tree P-Ideal Dichotomy Dowker space Singular Density Postprocessing function indecomposable filter regressive Souslin tree Universal Sequences S-Space Chang's conjecture Well-behaved magma approachability ideal Vanishing levels sap Strongly compact cardinal Dushnik-Miller SNR Diamond-sharp Whitehead Problem L-space Microscopic Approach ZFC construction incompactness very good scale Iterated forcing Martin's Axiom reflection principles b-scale middle diamond Commutative cancellative semigroups Ascent Path Slim tree weak Kurepa tree Absoluteness higher Baire space HOD Strong coloring Almost-disjoint family Uniformly coherent Mandelbrot set polarized partition relation Uniformly homogeneous stick Sierpinski's onto mapping principle Forcing Axioms Hereditarily Lindelöf space stationary hitting Erdos Cardinal Selective Ultrafilter Greatly Mahlo Parameterized proxy principle Forcing Cardinal function Singular cardinals combinatorics Weakly compact cardinal PFA(S)[S] Cohen real weak diamond unbounded function Partition relations for trees Local Club Condensation. Ostaszewski square O-space Subadditive 54G20 Successor of Singular Cardinal Nonspecial tree Subnormal ideal Diamond for trees club_AD OCA super-Souslin tree Monotonically far Closed coloring Ramsey theory over partitions Jonsson cardinal Uniformization Large Cardinals Partition Relations Commutative projection system tensor product graph Interval topology on trees Prikry-type forcing Hedetniemi's conjecture strongly bounded groups Poset Successor of Regular Cardinal perfectly normal stationary reflection Generalized Clubs Entangled linear order countably metacompact square principles full tree Was Ulam right? Lipschitz reduction Chromatic number Almost Souslin Reduced Power Foundations nonmeager set Fodor-type reflection Coherent tree Small forcing Sigma-Prikry diamond star Generalized descriptive set theory PFA Ascending path Souslin Tree Constructible Universe Knaster Filter reflection Fat stationary set Shelah's Strong Hypothesis weak square square Prevalent singular cardinals coloring number Analytic sets Club Guessing xbox Respecting tree Diamond Distributive tree Square-Brackets Partition Relations Minimal Walks Rock n' Roll ccc Antichain Precaliber positive partition relation Subtle tree property free Souslin tree
Tag Archives: stationary reflection
Openly generated Boolean algebras and the Fodor-type reflection principle
Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading
Posted in Compactness, Publications
Tagged 03E35, 03E55, 03E65, 03E75, 03G05, 06E05, Axiom R, Fodor-type reflection, free Boolean algebra, projective Boolean algebra, Shelah's Strong Hypothesis, stationary reflection
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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
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading
