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