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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
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- Square principles April 19, 2014
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### Keywords

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

# Tag Archives: Hindman’s Theorem

## 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