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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

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

# Tag Archives: Commutative cancellative semigroups

## 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