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- A strong form of König’s lemma October 21, 2017
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HOD Martin's Axiom Distributive tree Chang's conjecture Universal Sequences Club Guessing weak diamond P-Ideal Dichotomy Coherent tree Uniformly coherent Axiom R Partition Relations Successor of Singular Cardinal Postprocessing function Weakly compact cardinal Luzin set 20M14 Minimal Walks Poset Hedetniemi's conjecture middle diamond Rainbow sets free Boolean algebra Non-saturation Chromatic number Singular cardinals combinatorics Parameterized proxy principle super-Souslin tree Generalized Clubs Fat stationary set Nonspecial tree diamond star square principles very good scale Commutative cancellative semigroups Rado's conjecture Erdos-Hajnal graphs b-scale Stevo Todorcevic Reduced Power Prikry-type forcing sap Antichain Hereditarily Lindelöf space Souslin Tree Slim tree Cardinal function approachability ideal Almost Souslin Small forcing Square-Brackets Partition Relations Ostaszewski square PFA Prevalent singular cardinals L-space incompactness Constructible Universe Foundations Fodor-type reflection Forcing Shelah's Strong Hypothesis projective Boolean algebra 05A17 square Mandelbrot set Aronszajn tree Almost countably chromatic stationary reflection OCA weak square Ascent Path S-Space Fast club Rock n' Roll coloring number Erdos Cardinal tensor product graph PFA(S)[S] Successor of Regular Cardinal Kurepa Hypothesis Whitehead Problem 11P99 Singular coﬁnality xbox Absoluteness Hindman's Theorem Diamond Forcing Axioms Dushnik-Miller Large Cardinals polarized partition relation stationary hitting Jonsson cardinal reflection principles Microscopic Approach Selective Ultrafilter Singular Density ccc Knaster Almost-disjoint famiy Cardinal Invariants Uniformization Sakurai's Bell inequality Cohen real

# 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