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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

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

# 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