### Archives

### 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

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

# 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