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