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

# 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