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### 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

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

# 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