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Respecting tree Reduced Power Precaliber Successor of Singular Cardinal HOD Commutative cancellative semigroups Greatly Mahlo Generalized descriptive set theory Minimal Walks Ineffable cardinal square principles Filter reflection Knaster stationary hitting Rock n' Roll Fodor-type reflection ccc incompactness Diamond for trees Singular Density Chang's conjecture Whitehead Problem PFA(S)[S] free Souslin tree perfectly normal Diamond-sharp Well-behaved magma reflection principles Strongly Luzin set Singular cardinals combinatorics Successor of Regular Cardinal Jonsson cardinal polarized partition relation Amenable C-sequence Subadditive Antichain Microscopic Approach Ulam matrix Almost-disjoint family Cohen real Rado's conjecture Subnormal ideal xbox Erdos Cardinal projective Boolean algebra Souslin Tree C-sequence Interval topology on trees Lipschitz reduction strongly bounded groups Commutative projection system Mandelbrot set Sigma-Prikry Dushnik-Miller Small forcing unbounded function Shelah's Strong Hypothesis positive partition relation 54G20 Vanishing levels Partition Relations Subtle tree property Sierpinski's onto mapping principle Ramsey theory over partitions Closed coloring Hindman's Theorem Countryman line higher Baire space Martin's Axiom Ascending path AIM forcing b-scale Uniformly coherent Was Ulam right? Fast club coloring number super-Souslin tree tensor product graph Universal Sequences Nonspecial tree Forcing full tree Ascent Path Strongly compact cardinal Square-Brackets Partition Relations Absoluteness Postprocessing function Ostaszewski square Monotonically far Diamond Chromatic number Coherent tree Hedetniemi's conjecture diamond star Club Guessing regressive Souslin tree O-space Cardinal function Knaster and friends nonmeager set Strong coloring Dowker space Partition relations for trees Foundations Non-saturation approachability ideal Luzin set weak diamond Sakurai's Bell inequality S-Space Axiom R countably metacompact Generalized Clubs OCA Reflecting stationary set Poset Slim tree Iterated forcing Uniformization Rainbow sets GMA weak Kurepa tree ZFC construction stick Intersection model Distributive tree transformations Almost countably chromatic club_AD specializable Souslin tree Forcing with side conditions SNR Large Cardinals Cardinal Invariants P-Ideal Dichotomy L-space Hereditarily Lindelöf space Aronszajn tree Local Club Condensation. weak square stationary reflection PFA Uniformly homogeneous Constructible Universe Fat stationary set Prevalent singular cardinals Kurepa Hypothesis free Boolean algebra Forcing Axioms Open Access square very good scale Analytic sets Entangled linear order middle diamond Prikry-type forcing Erdos-Hajnal graphs Parameterized proxy principle Singular cofinality Subtle cardinal Almost Souslin sap Weakly compact cardinal Selective Ultrafilter indecomposable filter
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
