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

# 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