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### 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

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

# 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