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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

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

# 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