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