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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

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

# 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