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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

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

# Tag Archives: 05D10

## 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