### Archives

### Recent blog posts

- 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

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

# 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