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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

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

# Tag Archives: 11P99

## 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