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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

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

# Tag Archives: 05D10

## 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