### 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

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

# 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

## Set Theory Programme on Large Cardinals and Forcing, September 2013

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