### 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

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

# Tag Archives: 03E75

## Strong failures of higher analogs of Hindman’s Theorem

Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading

## 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

## Openly generated Boolean algebras and the Fodor-type reflection principle

Joint work with Sakaé Fuchino. Abstract: We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is $\aleph _2$-projective. Previously it was known that this … Continue reading