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