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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

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

# 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