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