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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

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