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