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### 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

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

# Tag Archives: 20M14

## 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