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Prikry-type forcing polarized partition relation Erdos Cardinal Souslin Tree Cardinal Invariants positive partition relation Uniformly coherent Entangled linear order middle diamond Dushnik-Miller countably metacompact Minimal Walks S-Space Uniformly homogeneous Successor of Regular Cardinal Almost countably chromatic specializable Souslin tree Constructible Universe Well-behaved magma unbounded function Partition Relations Singular Density Subadditive Prevalent singular cardinals Singular cofinality Small forcing Shelah's Strong Hypothesis approachability ideal Hereditarily Lindelöf space Luzin set Was Ulam right? Dowker space projective Boolean algebra Almost Souslin Subtle tree property Chang's conjecture C-sequence Forcing Ascent Path Parameterized proxy principle Erdos-Hajnal graphs Subtle cardinal free Souslin tree PFA Antichain Cardinal function Generalized Clubs sap Analytic sets ZFC construction Diamond OCA perfectly normal Sakurai's Bell inequality Mandelbrot set Lipschitz reduction Forcing with side conditions Ostaszewski square Universal Sequences indecomposable filter transformations Ulam matrix Commutative projection system PFA(S)[S] higher Baire space Countryman line Kurepa Hypothesis super-Souslin tree Singular cardinals combinatorics HOD Club Guessing Sierpinski's onto mapping principle Forcing Axioms Microscopic Approach Ramsey theory over partitions Whitehead Problem Foundations Ineffable cardinal Aronszajn tree Reduced Power Monotonically far Successor of Singular Cardinal square Rainbow sets coloring number Cohen real weak Kurepa tree Axiom R Greatly Mahlo Weakly compact cardinal stationary hitting Fodor-type reflection Selective Ultrafilter Baumgartner's square Filter reflection Nonspecial tree Open Access Intersection model Uniformization Poset strongly bounded groups xbox Amenable C-sequence Ascending path diamond star Vanishing levels Diamond for trees Almost-disjoint family incompactness Sigma-Prikry Diamond-sharp weak diamond Large Cardinals Commutative cancellative semigroups Rock n' Roll square principles Interval topology on trees Strong coloring Jonsson cardinal Strongly compact cardinal Knaster and friends Distributive tree Non-saturation nonmeager set Hindman's Theorem 54G20 Hedetniemi's conjecture Iterated forcing Martin's Axiom Precaliber Slim tree ccc club_AD regressive Souslin tree Rado's conjecture Partition relations for trees Subnormal ideal Fat stationary set Chromatic number Respecting tree stationary reflection SNR Local Club Condensation. Postprocessing function GMA AIM forcing Coherent tree Closed coloring stick O-space tensor product graph Reflecting stationary set weak square Generalized descriptive set theory P-Ideal Dichotomy Square-Brackets Partition Relations reflection principles free Boolean algebra Knaster L-space full tree b-scale Strongly Luzin set very good scale Fast club Absoluteness
Tag Archives: 05D10
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
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Entangled linear order, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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