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- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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