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