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- 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

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

# 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