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- Prikry forcing may add a Souslin tree June 12, 2016
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- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
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Erdos Cardinal xbox middle diamond Uniformization OCA Distributive tree Slim tree Square-Brackets Partition Relations Fast club Erdos-Hajnal graphs incompactness Prevalent singular cardinals Rock n' Roll Singular coﬁnality polarized partition relation Sakurai's Bell inequality b-scale ccc Aronszajn tree Cohen real Kurepa Hypothesis Fodor-type reflection very good scale Dushnik-Miller tensor product graph Jonsson cardinal Ascent Path weak square diamond star square principles Martin's Axiom Large Cardinals free Boolean algebra Successor of Singular Cardinal Successor of Regular Cardinal Partition Relations Foundations Souslin Tree Uniformly coherent projective Boolean algebra Weakly compact cardinal Rado's conjecture Almost countably chromatic Whitehead Problem Forcing Axioms square Universal Sequences Fat stationary set Antichain Selective Ultrafilter sap Generalized Clubs Rainbow sets Small forcing Cardinal Invariants Reduced Power Prikry-type forcing Hereditarily Lindelöf space Singular Density Poset 20M14 Microscopic Approach P-Ideal Dichotomy Axiom R Diamond Stevo Todorcevic Singular cardinals combinatorics Luzin set Cardinal function Hedetniemi's conjecture reflection principles coloring number approachability ideal HOD L-space Almost Souslin Non-saturation Chromatic number 05A17 Absoluteness 05D10 Nonspecial tree PFA Almost-disjoint famiy Knaster Postprocessing function 11P99 S-Space Chang's conjecture stationary reflection Club Guessing Commutative cancellative semigroups stationary hitting Parameterized proxy principle Ostaszewski square Forcing Coherent tree Constructible Universe weak diamond Minimal Walks Hindman's Theorem PFA(S)[S] Shelah's Strong Hypothesis Mandelbrot set

# 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