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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

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

# 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