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### Recent blog posts

- 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
- Square principles April 19, 2014

### Keywords

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

# Tag Archives: 05C76

## 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