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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

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

# Tag Archives: 20M14

## 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