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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

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

# Tag Archives: tensor product graph

## 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