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