### 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

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

# Tag Archives: Almost countably chromatic

## 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

## 2013 Set Theory Programme on Large Cardinals and Forcing

I gave an invited talk at the Large Cardinals and Forcing meeting, Erwin Schrödinger International Institute for Mathematical Physics, Vienna, September 23–27, 2013. Talk Title: Hedetniemi’s conjecture for uncountable graphs Abstract: It is proved that in Godel’s constructible universe, for … Continue reading

Posted in Invited Talks
Tagged Almost countably chromatic, Chromatic number, Hedetniemi's conjecture
1 Comment

## Chromatic numbers of graphs – large gaps

Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading

Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
6 Comments