### 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

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

# Tag Archives: Hindman’s Theorem

## 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