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Erdos-Hajnal graphs Fat stationary set middle diamond Hedetniemi's conjecture Forcing Axioms Axiom R Almost-disjoint family approachability ideal Distributive tree Selective Ultrafilter Universal Sequences Uniformly coherent ZFC construction Weakly compact cardinal Large Cardinals weak Kurepa tree full tree Hindman's Theorem regressive Souslin tree Iterated forcing Fodor-type reflection square principles Luzin set countably metacompact Microscopic Approach Filter reflection diamond star Ulam matrix Chromatic number polarized partition relation transformations free Souslin tree Singular cofinality Closed coloring Diamond for trees projective Boolean algebra Antichain Parameterized proxy principle Almost Souslin Singular Density Absoluteness Uniformly homogeneous Diamond-sharp Postprocessing function Martin's Axiom AIM forcing Club Guessing Open Access C-sequence SNR Poset 54G20 positive partition relation coloring number Partition Relations Rock n' Roll Dowker space Commutative cancellative semigroups Was Ulam right Reflecting stationary set Knaster Whitehead Problem Sigma-Prikry Forcing Cardinal function Subadditive ccc Almost countably chromatic free Boolean algebra sap Ostaszewski square Prevalent singular cardinals Successor of Regular Cardinal Mandelbrot set Amenable C-sequence Vanishing levels Foundations Uniformization super-Souslin tree Hereditarily Lindelöf space indecomposable ultrafilter stationary reflection club_AD Cardinal Invariants Local Club Condensation. Sakurai's Bell inequality specializable Souslin tree Ramsey theory over partitions Ineffable cardinal HOD Minimal Walks Generalized descriptive set theory Knaster and friends higher Baire space O-space reflection principles PFA Non-saturation Coherent tree Precaliber Kurepa Hypothesis Cohen real Nonspecial tree Dushnik-Miller Reduced Power Well-behaved magma OCA incompactness Ascent Path P-Ideal Dichotomy Analytic sets S-Space Rado's conjecture Successor of Singular Cardinal stationary hitting Singular cardinals combinatorics nonmeager set unbounded function square Strong coloring weak diamond Shelah's Strong Hypothesis Lipschitz reduction very good scale PFA(S)[S] Strongly Luzin set Slim tree Aronszajn tree Subtle cardinal Diamond Square-Brackets Partition Relations Rainbow sets Subnormal ideal Fast club stick Souslin Tree Sierpinski's onto mapping principle Jonsson cardinal Subtle tree property GMA Prikry-type forcing strongly bounded groups weak square Erdos Cardinal L-space Constructible Universe Chang's conjecture Greatly Mahlo tensor product graph Small forcing xbox Generalized Clubs b-scale
Tag Archives: Constructible Universe
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
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INFTY Final Conference, March 2014
I gave an invited talk at the INFTY Final Conference meeting, Bonn, March 4-7, 2014. [Curiosity: Georg Cantor was born March 3, 1845] Title: Same Graph, Different Universe. Abstract: In a paper from 1998, answering a question of Hajnal, Soukup … Continue reading
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