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### Recent blog posts

- 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

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

# 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