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