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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
- Genearlizations 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

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

# Tag Archives: 05D10

## 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