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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
- 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

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

# 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