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- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

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Almost-disjoint famiy Parameterized proxy principle Ascent Path Knaster Erdos Cardinal Sakurai's Bell inequality Successor of Singular Cardinal stationary hitting 11P99 diamond star weak square Non-saturation 05A17 Absoluteness Generalized Clubs Prevalent singular cardinals Partition Relations Commutative cancellative semigroups Antichain weak diamond approachability ideal Chromatic number sap Singular Density Square-Brackets Partition Relations Successor of Regular Cardinal Jonsson cardinal stationary reflection Hedetniemi's conjecture xbox Whitehead Problem Constructible Universe Club Guessing Dushnik-Miller Diamond Cardinal Invariants Forcing L-space OCA Singular coﬁnality reflection principles S-Space Reduced Power Aronszajn tree Cardinal function Kurepa Hypothesis 20M14 Weakly compact cardinal Fodor-type reflection square Small forcing 05D10 Universal Sequences Almost Souslin tensor product graph middle diamond Coherent tree Poset Fat stationary set Rock n' Roll Singular Cofinality Martin's Axiom Hindman's Theorem Selective Ultrafilter projective Boolean algebra Minimal Walks Hereditarily Lindelöf space Singular cardinals combinatorics Shelah's Strong Hypothesis polarized partition relation Slim tree Fast club coloring number Almost countably chromatic Large Cardinals very good scale PFA(S)[S] Microscopic Approach PFA Forcing Axioms Axiom R incompactness Prikry-type forcing Cohen real Chang's conjecture Ostaszewski square Foundations Mandelbrot set Uniformization ccc b-scale HOD Rainbow sets P-Ideal Dichotomy Souslin Tree Rado's conjecture Stevo Todorcevic Erdos-Hajnal graphs free Boolean algebra

# 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