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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

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

# Tag Archives: Jonsson cardinal

## 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