### Archives

### Recent blog posts

- 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
- Partitioning the club guessing January 22, 2014

### Keywords

polarized partition relation Universal Sequences projective Boolean algebra 20M14 xbox tensor product graph Mandelbrot set free Boolean algebra square principles ccc Slim tree Uniformization Singular coﬁnality L-space Martin's Axiom Club Guessing weak diamond Non-saturation reflection principles sap Whitehead Problem 05A17 05D10 Erdos-Hajnal graphs Fodor-type reflection b-scale Weakly compact cardinal Chromatic number Hedetniemi's conjecture OCA Stevo Todorcevic coloring number Parameterized proxy principle Partition Relations Successor of Regular Cardinal middle diamond Nonspecial tree Foundations P-Ideal Dichotomy Rock n' Roll Shelah's Strong Hypothesis Poset Singular cardinals combinatorics approachability ideal diamond star Distributive tree Square-Brackets Partition Relations Constructible Universe Coherent tree Chang's conjecture Antichain Rado's conjecture Absoluteness Ascent Path square Forcing Microscopic Approach Ostaszewski square Cardinal Invariants Large Cardinals Commutative cancellative semigroups Fat stationary set Postprocessing function Jonsson cardinal Hereditarily Lindelöf space S-Space Almost-disjoint famiy Axiom R Dushnik-Miller Successor of Singular Cardinal HOD Prikry-type forcing Prevalent singular cardinals incompactness Minimal Walks Aronszajn tree Sakurai's Bell inequality Forcing Axioms Fast club Kurepa Hypothesis Rainbow sets Small forcing Singular Density weak square Generalized Clubs Uniformly coherent Almost countably chromatic Erdos Cardinal Almost Souslin Cardinal function Souslin Tree Knaster stationary reflection Selective Ultrafilter stationary hitting Diamond 11P99 PFA PFA(S)[S] very good scale Reduced Power Cohen real Hindman's Theorem

# 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