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