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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
- Happy new jewish year! September 24, 2014
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Rainbow sets Club Guessing Aronszajn tree Partition Relations Almost-disjoint famiy Slim tree free Boolean algebra xbox Prevalent singular cardinals Ostaszewski square L-space S-Space Minimal Walks Ascent Path stationary hitting specializable Souslin tree Hereditarily Lindelöf space Parameterized proxy principle weak diamond Almost Souslin ccc Microscopic Approach Singular coﬁnality Diamond Fast club Non-saturation OCA Chromatic number reflection principles Uniformly coherent Almost countably chromatic very good scale Antichain Nonspecial tree Constructible Universe Mandelbrot set coloring number Successor of Singular Cardinal incompactness Rado's conjecture Successor of Regular Cardinal tensor product graph Knaster Hindman's Theorem Cardinal Invariants b-scale 11P99 Erdos Cardinal Absoluteness Weakly compact cardinal Forcing Axioms square principles Foundations Souslin Tree projective Boolean algebra Stevo Todorcevic P-Ideal Dichotomy weak square Shelah's Strong Hypothesis Martin's Axiom Forcing middle diamond Universal Sequences Dushnik-Miller stationary reflection Postprocessing function Fodor-type reflection Coherent tree polarized partition relation diamond star Cohen real HOD Jonsson cardinal free Souslin tree Poset Fat stationary set approachability ideal Whitehead Problem Kurepa Hypothesis Prikry-type forcing Chang's conjecture Small forcing Cardinal function Erdos-Hajnal graphs 05A17 Singular cardinals combinatorics Uniformization Reduced Power Selective Ultrafilter Rock n' Roll PFA(S)[S] Large Cardinals Axiom R Square-Brackets Partition Relations Generalized Clubs Commutative cancellative semigroups Singular Density Sakurai's Bell inequality Distributive tree Luzin set super-Souslin tree sap PFA square Hedetniemi's conjecture

# 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