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- A strong form of König’s lemma October 21, 2017
- 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
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Postprocessing function Generalized Clubs Poset Sakurai's Bell inequality Rock n' Roll specializable Souslin tree square xbox Large Cardinals Rainbow sets Forcing Axioms Ostaszewski square Club Guessing Coherent tree Partition Relations Selective Ultrafilter Absoluteness Chromatic number Martin's Axiom Fast club Universal Sequences HOD Cohen real stationary reflection Stevo Todorcevic Cardinal Invariants free Boolean algebra Knaster Almost-disjoint famiy Axiom R Almost countably chromatic projective Boolean algebra weak diamond 05A17 Aronszajn tree PFA ccc Hedetniemi's conjecture 11P99 Mandelbrot set Prikry-type forcing Minimal Walks Chang's conjecture approachability ideal PFA(S)[S] Shelah's Strong Hypothesis Souslin Tree Small forcing free Souslin tree Forcing Square-Brackets Partition Relations Dushnik-Miller Luzin set super-Souslin tree Slim tree Commutative cancellative semigroups stationary hitting Jonsson cardinal Kurepa Hypothesis Prevalent singular cardinals Successor of Singular Cardinal Cardinal function Uniformization square principles diamond star Hindman's Theorem Almost Souslin Antichain Rado's conjecture Hereditarily Lindelöf space Nonspecial tree polarized partition relation very good scale L-space S-Space Successor of Regular Cardinal Singular coﬁnality OCA Erdos Cardinal b-scale Singular cardinals combinatorics Distributive tree Uniformly coherent Fat stationary set P-Ideal Dichotomy Weakly compact cardinal Parameterized proxy principle coloring number tensor product graph Reduced Power Erdos-Hajnal graphs incompactness sap Diamond reflection principles Microscopic Approach weak square Foundations Non-saturation middle diamond Ascent Path Fodor-type reflection Singular Density Constructible Universe Whitehead Problem

# 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