### 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

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

# 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