### 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

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

# 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