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- A strong form of König’s lemma October 21, 2017
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- The reflection principle $R_2$ May 20, 2016
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### Keywords

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

# 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