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