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