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