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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

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

# 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