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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
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### Keywords

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

# 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