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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

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

# Tag Archives: 20M14

## 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