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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
- 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

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

# 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