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