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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

Slim tree coloring number Successor of Singular Cardinal Prikry-type forcing diamond star reflection principles PFA(S)[S] Knaster Chang's conjecture Singular cardinals combinatorics Uniformization Rado's conjecture Ostaszewski square Dushnik-Miller Hereditarily Lindelöf space 11P99 Nonspecial tree approachability ideal Poset weak diamond HOD Small forcing PFA Ascent Path tensor product graph Forcing Hindman's Theorem Antichain free Boolean algebra incompactness Almost Souslin Non-saturation Hedetniemi's conjecture Singular Density Microscopic Approach Uniformly coherent Fat stationary set Prevalent singular cardinals Selective Ultrafilter Whitehead Problem 05A17 L-space ccc Cohen real stationary hitting Successor of Regular Cardinal Shelah's Strong Hypothesis Cardinal Invariants Partition Relations projective Boolean algebra Luzin set Cardinal function Jonsson cardinal middle diamond Club Guessing Universal Sequences sap b-scale Singular coﬁnality Aronszajn tree Sakurai's Bell inequality Stevo Todorcevic Constructible Universe Parameterized proxy principle Diamond Coherent tree Almost-disjoint famiy Mandelbrot set Reduced Power very good scale Axiom R Souslin Tree OCA Postprocessing function Distributive tree Almost countably chromatic Erdos-Hajnal graphs Foundations Fodor-type reflection Chromatic number Large Cardinals Forcing Axioms Weakly compact cardinal weak square xbox square Absoluteness Commutative cancellative semigroups Erdos Cardinal 20M14 Generalized Clubs Kurepa Hypothesis polarized partition relation Square-Brackets Partition Relations 05D10 P-Ideal Dichotomy Fast club stationary reflection Rock n' Roll Rainbow sets square principles S-Space Minimal Walks Martin's Axiom

# Tag Archives: 05A17

## 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