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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

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

# 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