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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

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

# 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