### 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

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

# Tag Archives: 05A17

## 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