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