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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

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

# Tag Archives: 11P99

## 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