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Rado's conjecture Souslin Tree Precaliber Small forcing Fodor-type reflection Subtle tree property PFA(S)[S] Ulam matrix Diamond for trees stationary hitting Minimal Walks Subnormal ideal Whitehead Problem Cardinal function Hereditarily Lindelöf space Rock n' Roll GMA Was Ulam right? Forcing weak square Singular cofinality Local Club Condensation. Fast club Amenable C-sequence Aronszajn tree Antichain Entangled linear order Erdos Cardinal Uniformly homogeneous ZFC construction Uniformly coherent Partition Relations Commutative cancellative semigroups xbox 54G20 Closed coloring Ostaszewski square free Boolean algebra Forcing with side conditions Strongly compact cardinal Singular cardinals combinatorics Sierpinski's onto mapping principle Almost-disjoint family Baumgartner's square Foundations Postprocessing function Universal Sequences Chang's conjecture Iterated forcing Strongly Luzin set Ramsey theory over partitions Prikry-type forcing Cardinal Invariants Generalized Clubs diamond star Prevalent singular cardinals stick Uniformization stationary reflection Fat stationary set Filter reflection Ascent Path Luzin set Greatly Mahlo tensor product graph HOD Mandelbrot set regressive Souslin tree Partition relations for trees Generalized descriptive set theory Knaster and friends positive partition relation Parameterized proxy principle Erdos-Hajnal graphs indecomposable filter Subtle cardinal specializable Souslin tree polarized partition relation PFA Lipschitz reduction Distributive tree weak Kurepa tree weak diamond Sigma-Prikry Ascending path Intersection model Almost Souslin Commutative projection system Kurepa Hypothesis Weakly compact cardinal Microscopic Approach Nonspecial tree Reflecting stationary set b-scale S-Space Knaster Interval topology on trees Well-behaved magma Forcing Axioms Respecting tree Absoluteness Martin's Axiom unbounded function Club Guessing Square-Brackets Partition Relations perfectly normal Analytic sets Open Access Axiom R free Souslin tree Large Cardinals incompactness higher Baire space Monotonically far square Ineffable cardinal Reduced Power Dowker space Hindman's Theorem middle diamond ccc Rainbow sets projective Boolean algebra Selective Ultrafilter C-sequence Poset SNR Strong coloring Coherent tree Jonsson cardinal club_AD Vanishing levels Shelah's Strong Hypothesis P-Ideal Dichotomy Subadditive sap Dushnik-Miller Non-saturation Diamond full tree Successor of Regular Cardinal countably metacompact strongly bounded groups square principles O-space L-space approachability ideal transformations coloring number Hedetniemi's conjecture nonmeager set Successor of Singular Cardinal Singular Density Chromatic number reflection principles very good scale Sakurai's Bell inequality super-Souslin tree OCA Cohen real Almost countably chromatic Constructible Universe Countryman line AIM forcing Slim tree Diamond-sharp
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
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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 $\kappa$, there exist graphs $\mathcal G$ and $\mathcal H$ of size and chromatic number $\kappa$, for which the tensor product graph $\mathcal G\times\mathcal H$ is countably chromatic. … Continue reading
Chromatic numbers of graphs – large gaps
Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
6 Comments
