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Poset square Was Ulam right Minimal Walks Hereditarily Lindelöf space Uniformization Uniformly coherent Commutative cancellative semigroups Parameterized proxy principle Prevalent singular cardinals ZFC construction AIM forcing Foundations Uniformly homogeneous Mandelbrot set stationary hitting Square-Brackets Partition Relations Ascent Path Martin's Axiom Subadditive Sierpinski's onto mapping principle transformations Luzin set Partition Relations Singular Density Hindman's Theorem reflection principles Non-saturation Absoluteness projective Boolean algebra countably metacompact Fat stationary set Forcing Axioms diamond star S-Space Sigma-Prikry Open Access Ulam matrix OCA Knaster regressive Souslin tree Generalized Clubs Strong coloring Rock n' Roll P-Ideal Dichotomy Axiom R Postprocessing function Chromatic number higher Baire space Rainbow sets Souslin Tree Coherent tree Microscopic Approach Ramsey theory over partitions Sakurai's Bell inequality Cardinal function Hedetniemi's conjecture Club Guessing strongly bounded groups Fodor-type reflection Almost countably chromatic C-sequence Successor of Regular Cardinal Shelah's Strong Hypothesis Well-behaved magma SNR sap Selective Ultrafilter nonmeager set tensor product graph Dowker space free Souslin tree Antichain Diamond for trees Subnormal ideal Singular cardinals combinatorics Cohen real Slim tree middle diamond weak square polarized partition relation Kurepa Hypothesis PFA Weakly compact cardinal Vanishing levels Strongly Luzin set full tree Small forcing Nonspecial tree Subtle cardinal Jonsson cardinal Precaliber Dushnik-Miller incompactness Lipschitz reduction Greatly Mahlo Distributive tree super-Souslin tree Fast club L-space stationary reflection weak diamond Singular cofinality PFA(S)[S] Prikry-type forcing coloring number xbox Erdos-Hajnal graphs Diamond-sharp O-space Iterated forcing Local Club Condensation. GMA Filter reflection ccc Knaster and friends Large Cardinals Subtle tree property Almost Souslin square principles unbounded function stick indecomposable ultrafilter Amenable C-sequence Successor of Singular Cardinal Reduced Power approachability ideal specializable Souslin tree club_AD Universal Sequences 54G20 Analytic sets Whitehead Problem Closed coloring HOD Aronszajn tree Rado's conjecture Constructible Universe Generalized descriptive set theory Forcing very good scale Diamond b-scale Erdos Cardinal Cardinal Invariants Almost-disjoint family positive partition relation Chang's conjecture Reflecting stationary set free Boolean algebra Ostaszewski square Ineffable cardinal
Tag Archives: Chang’s conjecture
Reflection on the coloring and chromatic numbers
Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Chang's conjecture, Chromatic number, coloring number, Fodor-type reflection, incompactness, Iterated forcing, Parameterized proxy principle, Postprocessing function, Rado's conjecture, square, stationary reflection
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Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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