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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

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

# 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