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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

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

# 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