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