### Archives

### Recent blog posts

- 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

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

# 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
10 Comments

## 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