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Chang's conjecture Strong coloring Prikry-type forcing Jonsson cardinal Forcing with side conditions Well-behaved magma Iterated forcing free Souslin tree Ramsey theory over partitions indecomposable filter Diamond for trees weak square Singular Density Commutative projection system Almost countably chromatic Luzin set AIM forcing Rado's conjecture regressive Souslin tree Whitehead Problem PFA(S)[S] Aronszajn tree Singular cofinality Commutative cancellative semigroups Small forcing Successor of Singular Cardinal projective Boolean algebra L-space HOD Slim tree square Analytic sets Diamond-sharp Non-saturation Reflecting stationary set Universal Sequences Rock n' Roll countably metacompact Vanishing levels Antichain higher Baire space Ulam matrix coloring number Cardinal Invariants Almost Souslin Erdos Cardinal Club Guessing Sigma-Prikry Knaster and friends Subadditive Filter reflection Subtle tree property Fat stationary set Intersection model Successor of Regular Cardinal Reduced Power Forcing Axioms Interval topology on trees Prevalent singular cardinals square principles Forcing Singular cardinals combinatorics Monotonically far Martin's Axiom Dushnik-Miller OCA Closed coloring P-Ideal Dichotomy tensor product graph Knaster polarized partition relation b-scale Ostaszewski square positive partition relation Souslin Tree super-Souslin tree Precaliber Kurepa Hypothesis middle diamond Cardinal function Large Cardinals free Boolean algebra Weakly compact cardinal Ineffable cardinal unbounded function Diamond stationary reflection Cohen real weak Kurepa tree Lipschitz reduction Shelah's Strong Hypothesis Sierpinski's onto mapping principle Dowker space diamond star Hindman's Theorem Greatly Mahlo Fodor-type reflection Respecting tree Constructible Universe Local Club Condensation. Sakurai's Bell inequality Distributive tree Generalized descriptive set theory weak diamond incompactness PFA Uniformly coherent Amenable C-sequence Square-Brackets Partition Relations ZFC construction perfectly normal Parameterized proxy principle Erdos-Hajnal graphs O-space Generalized Clubs Entangled linear order reflection principles specializable Souslin tree stationary hitting Chromatic number Ascending path Mandelbrot set Ascent Path Axiom R sap Was Ulam right? Almost-disjoint family ccc approachability ideal club_AD SNR Uniformization Poset Rainbow sets Subnormal ideal Partition Relations Absoluteness C-sequence Strongly compact cardinal 54G20 S-Space Selective Ultrafilter Hedetniemi's conjecture Hereditarily Lindelöf space xbox Microscopic Approach Strongly Luzin set strongly bounded groups Fast club Uniformly homogeneous nonmeager set GMA Nonspecial tree full tree Minimal Walks Subtle cardinal Countryman line Foundations Postprocessing function Open Access transformations Coherent tree stick very good scale
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A counterexample related to a theorem of Komjáth and Weiss
Joint work with Rodrigo Rey Carvalho. Abstract. In a paper from 1987, Komjath and Weiss proved that for every regular topological space $X$ of character less than $\mathfrak b$, if $X\rightarrow(\text{top }{\omega+1})^1_\omega$, then $X\rightarrow(\text{top }{\alpha})^1_\omega$ for all $\alpha<\omega_1$. In addition, … Continue reading
Posted in Partition Relations, Preprints, Topology
Tagged 03E02, 54G20, Open Access, Prikry-type forcing, ZFC construction
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