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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

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

# 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