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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
- Generalizations 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

### Keywords

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

# 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