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