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Subtle tree property regressive Souslin tree Parameterized proxy principle Filter reflection HOD full tree xbox Interval topology on trees indecomposable filter Erdos Cardinal Whitehead Problem tensor product graph stationary reflection strongly bounded groups Well-behaved magma Sierpinski's onto mapping principle Successor of Regular Cardinal club_AD Sigma-Prikry Subnormal ideal reflection principles Cardinal function ZFC construction Non-saturation Countryman line Ulam matrix L-space Successor of Singular Cardinal Ostaszewski square positive partition relation transformations unbounded function Martin's Axiom middle diamond Reduced Power Entangled linear order Hereditarily Lindelöf space Partition Relations Singular cofinality square Vanishing levels Fodor-type reflection Uniformly coherent Chang's conjecture Luzin set Microscopic Approach Partition relations for trees Square-Brackets Partition Relations Monotonically far SNR Distributive tree Strong coloring Prevalent singular cardinals Intersection model perfectly normal Postprocessing function Axiom R Open Access Local Club Condensation. free Boolean algebra Singular cardinals combinatorics Respecting tree Jonsson cardinal square principles approachability ideal Subadditive Rock n' Roll Constructible Universe coloring number weak square Universal Sequences Shelah's Strong Hypothesis Large Cardinals Forcing Axioms P-Ideal Dichotomy countably metacompact 54G20 Hedetniemi's conjecture b-scale GMA PFA(S)[S] stationary hitting Mandelbrot set Fast club specializable Souslin tree Generalized Clubs Sakurai's Bell inequality Almost countably chromatic sap Ascent Path Antichain Slim tree Dushnik-Miller higher Baire space Minimal Walks Forcing Ramsey theory over partitions Foundations Strongly Luzin set Closed coloring Precaliber PFA Uniformly homogeneous AIM forcing C-sequence free Souslin tree S-Space Fat stationary set Kurepa Hypothesis Chromatic number Uniformization ccc Diamond Ineffable cardinal OCA Erdos-Hajnal graphs Commutative projection system stick Iterated forcing Aronszajn tree Absoluteness Commutative cancellative semigroups Diamond-sharp diamond star Lipschitz reduction Singular Density Knaster and friends nonmeager set Club Guessing O-space weak Kurepa tree Was Ulam right? projective Boolean algebra Forcing with side conditions Small forcing Ascending path Almost Souslin polarized partition relation very good scale weak diamond Knaster Reflecting stationary set Coherent tree Subtle cardinal Generalized descriptive set theory Souslin Tree Strongly compact cardinal Poset super-Souslin tree incompactness Rado's conjecture Cardinal Invariants Selective Ultrafilter Amenable C-sequence Dowker space Weakly compact cardinal Almost-disjoint family Cohen real Diamond for trees Analytic sets Rainbow sets Greatly Mahlo Prikry-type forcing Nonspecial tree Hindman's Theorem
Category Archives: Compactness
Chromatic numbers of graphs – large gaps
Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
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A topological reflection principle equivalent to Shelah’s strong hypothesis
Abstract: We notice that Shelah’s Strong Hypothesis (SSH) is equivalent to the following reflection principle: Suppose $\mathbb X$ is an (infinite) first-countable space whose density is a regular cardinal, $\kappa$. If every separable subspace of $\mathbb X$ is of cardinality at most … Continue reading
Posted in Compactness, Publications, Topology
Tagged 03E04, 03E65, 54G15, Open Access, Shelah's Strong Hypothesis
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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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