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