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

# Tag Archives: Hindman’s Theorem

## 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