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square principles HOD Chang's conjecture Cohen real Ostaszewski square polarized partition relation AIM forcing coloring number Generalized descriptive set theory Ascent Path Successor of Singular Cardinal Non-saturation stick club_AD O-space OCA C-sequence Cardinal function weak square Almost countably chromatic Diamond Open Access Almost Souslin PFA(S)[S] Constructible Universe Amenable C-sequence ZFC construction Commutative cancellative semigroups Filter reflection Countryman line Rainbow sets Minimal Walks Subtle tree property Prikry-type forcing diamond star Analytic sets Respecting tree Uniformization Generalized Clubs Square-Brackets Partition Relations Knaster b-scale Dowker space Large Cardinals Partition Relations Forcing Axioms Parameterized proxy principle projective Boolean algebra Postprocessing function Strong coloring Iterated forcing Commutative projection system Subnormal ideal positive partition relation Dushnik-Miller super-Souslin tree Singular cardinals combinatorics Diamond for trees xbox Weakly compact cardinal incompactness Whitehead Problem Shelah's Strong Hypothesis Fat stationary set Almost-disjoint family Reflecting stationary set Microscopic Approach Strongly Luzin set strongly bounded groups L-space Strongly compact cardinal Lipschitz reduction Closed coloring specializable Souslin tree square Distributive tree Luzin set Ineffable cardinal transformations regressive Souslin tree Foundations Well-behaved magma tensor product graph sap GMA Knaster and friends Intersection model Uniformly coherent Cardinal Invariants 54G20 Martin's Axiom Subtle cardinal Nonspecial tree stationary hitting Was Ulam right? free Souslin tree reflection principles Fast club stationary reflection higher Baire space Club Guessing full tree Axiom R SNR Rock n' Roll Forcing Poset Local Club Condensation. Jonsson cardinal Fodor-type reflection Vanishing levels Slim tree Absoluteness Souslin Tree Ulam matrix Sigma-Prikry Coherent tree middle diamond Ramsey theory over partitions Singular Density Successor of Regular Cardinal Prevalent singular cardinals Precaliber P-Ideal Dichotomy Hereditarily Lindelöf space unbounded function very good scale Kurepa Hypothesis Uniformly homogeneous countably metacompact indecomposable ultrafilter Hedetniemi's conjecture Aronszajn tree free Boolean algebra ccc Erdos-Hajnal graphs Diamond-sharp Subadditive Chromatic number Erdos Cardinal Sierpinski's onto mapping principle Small forcing Mandelbrot set Sakurai's Bell inequality S-Space PFA Universal Sequences weak diamond Antichain Singular cofinality Hindman's Theorem nonmeager set Reduced Power Rado's conjecture weak Kurepa tree Selective Ultrafilter Greatly Mahlo approachability ideal
Tag Archives: 05C15
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
Same Graph, Different Universe
Abstract. May the same graph admit two different chromatic numbers in two different universes? how about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Godel’s constructible … Continue reading
Posted in Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, approachability ideal, Chromatic number, Constructible Universe, Forcing, Ostaszewski square
10 Comments
Hedetniemi’s conjecture for uncountable graphs
Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal
Chromatic numbers of graphs – large gaps
Abstract. We say that a graph
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
6 Comments
