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