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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

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

# Tag Archives: 05D10

## 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