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