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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

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

# 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