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

# Tag Archives: Commutative cancellative semigroups

## 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