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