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