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### 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

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

# Tag Archives: 11P99

## 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