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