Archives
Keywords
Intersection model Ineffable cardinal unbounded function Fodor-type reflection club_AD weak diamond transformations sap Prevalent singular cardinals b-scale Partition Relations Minimal Walks Diamond Poset tensor product graph ccc Open Access middle diamond Vanishing levels Constructible Universe Local Club Condensation. square Sigma-Prikry Diamond for trees Foundations Club Guessing Greatly Mahlo Subnormal ideal Large Cardinals Subtle cardinal Singular Density Generalized Clubs nonmeager set ZFC construction Souslin Tree regressive Souslin tree Erdos-Hajnal graphs Diamond-sharp Reduced Power Slim tree polarized partition relation Fat stationary set Almost countably chromatic Successor of Singular Cardinal Filter reflection Absoluteness Chang's conjecture free Souslin tree Whitehead Problem Subtle tree property Generalized descriptive set theory Uniformly homogeneous specializable Souslin tree Analytic sets Coherent tree Cardinal function Commutative cancellative semigroups Rado's conjecture positive partition relation Erdos Cardinal diamond star Luzin set Aronszajn tree SNR indecomposable ultrafilter Dowker space Forcing Axioms Martin's Axiom Amenable C-sequence approachability ideal Postprocessing function Fast club Countryman line Mandelbrot set Microscopic Approach stationary hitting S-Space stationary reflection Closed coloring P-Ideal Dichotomy Iterated forcing Kurepa Hypothesis Strongly Luzin set super-Souslin tree Lipschitz reduction Almost Souslin L-space higher Baire space OCA Cohen real weak square Commutative projection system xbox Ascent Path Antichain Weakly compact cardinal Almost-disjoint family Prikry-type forcing Forcing Hindman's Theorem HOD Universal Sequences Singular cofinality O-space Chromatic number full tree Ramsey theory over partitions strongly bounded groups PFA Knaster and friends incompactness Precaliber Strong coloring free Boolean algebra weak Kurepa tree Dushnik-Miller Was Ulam right? Ostaszewski square Hereditarily Lindelöf space 54G20 Sierpinski's onto mapping principle reflection principles Sakurai's Bell inequality Non-saturation Successor of Regular Cardinal Respecting tree AIM forcing Cardinal Invariants Well-behaved magma Axiom R Square-Brackets Partition Relations Parameterized proxy principle Rock n' Roll Selective Ultrafilter PFA(S)[S] Small forcing Uniformization Strongly compact cardinal Rainbow sets projective Boolean algebra Singular cardinals combinatorics Nonspecial tree C-sequence countably metacompact GMA Distributive tree Ulam matrix Shelah's Strong Hypothesis Hedetniemi's conjecture very good scale Knaster stick Uniformly coherent Reflecting stationary set Jonsson cardinal Subadditive coloring number square principles
Tag Archives: 05C63
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
