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

# 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