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Model theory of modules over a serial ring

Paul C. Eklof & Ivo Herzog

Annals of Pure and Applied Logic 72 (2):145-176 (1995)

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Vapnik–Chervonenkis Density in Some Theories without the Independence Property, II.Matthias Aschenbrenner, Alf Dolich, Deirdre Haskell, Dugald Macpherson & Sergei Starchenko - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):311-363.details We study the Vapnik–Chervonenkis density of definable families in certain stable first-order theories. In particular, we obtain uniform bounds on the VC density of definable families in finite $\mathrm {U}$-rank theories without the finite cover property, and we characterize those abelian groups for which there exist uniform bounds on the VC density of definable families. Download Export citation Bookmark 11 citations
(1 other version)Vaught's conjecture for modules over a serial ring.Vera Puninskaya - 2000 - Journal of Symbolic Logic 65 (1):155-163.details It is proved that Vaught's conjecture is true for modules over an arbitrary countable serial ring. It follows from the structural result that every module with few models over a (countable) serial ring is ω-stable. Download Export citation Bookmark
Decidability of the theory of modules over prüfer domains with infinite residue fields.Lorna Gregory, Sonia L’Innocente, Gena Puninski & Carlo Toffalori - 2018 - Journal of Symbolic Logic 83 (4):1391-1412.details Download Export citation Bookmark 1 citation
Decidability of the theory of modules over Prüfer domains with dense value groups.Lorna Gregory, Sonia L'Innocente & Carlo Toffalori - 2019 - Annals of Pure and Applied Logic 170 (12):102719.details We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary. Download Export citation Bookmark

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