### 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
- Genearlizations 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

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

# Tag Archives: 20M14

## 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