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- A strong form of König’s lemma October 21, 2017
- 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
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Ostaszewski square projective Boolean algebra Knaster Postprocessing function Antichain tensor product graph b-scale reflection principles Uniformly coherent Axiom R diamond star Microscopic Approach Singular Density weak square Almost Souslin Martin's Axiom Rock n' Roll super-Souslin tree Cohen real Singular coﬁnality OCA Partition Relations Prikry-type forcing Hindman's Theorem Ascent Path Chromatic number sap incompactness Singular cardinals combinatorics free Boolean algebra Chang's conjecture Absoluteness Rainbow sets Rado's conjecture Aronszajn tree Successor of Singular Cardinal Cardinal function Mandelbrot set Luzin set Selective Ultrafilter Whitehead Problem very good scale Square-Brackets Partition Relations Forcing Axioms middle diamond Successor of Regular Cardinal Poset Minimal Walks Generalized Clubs Jonsson cardinal xbox PFA Prevalent singular cardinals Fast club Constructible Universe polarized partition relation Large Cardinals Club Guessing S-Space Commutative cancellative semigroups 05A17 PFA(S)[S] Erdos-Hajnal graphs Coherent tree Distributive tree Non-saturation Shelah's Strong Hypothesis 11P99 square principles Sakurai's Bell inequality Hereditarily Lindelöf space square Hedetniemi's conjecture Diamond Almost-disjoint famiy coloring number Stevo Todorcevic Fat stationary set L-space Erdos Cardinal Foundations Dushnik-Miller ccc Nonspecial tree 20M14 approachability ideal Forcing Small forcing Reduced Power stationary reflection weak diamond Weakly compact cardinal Cardinal Invariants Parameterized proxy principle Slim tree Almost countably chromatic P-Ideal Dichotomy Universal Sequences HOD Fodor-type reflection Souslin Tree Kurepa Hypothesis Uniformization stationary hitting

# 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