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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

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

# Tag Archives: 05A17

## 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