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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

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

# Tag Archives: 05A17

## 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