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