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