A note on groups definable in difference fields

DOI10.1090/S0002-9939-01-06004-XzbMath0983.03033MaRDI QIDQ2750906

Piotr Kowalski, Anand Pillay

Publication date: 21 October 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

differential fielddefinable groupdifference field\(\star\)-definable group

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) Differential and difference algebra (12H99) Model theory of fields (12L12)

Related Items (9)

Model theory of endomorphisms of separably closed fields ⋮ Graphons arising from graphs definable over finite fields ⋮ On subgroups of semi-abelian varieties defined by difference equations ⋮ Difference Galois theory of linear differential equations ⋮ Almost-simple affine difference algebraic groups ⋮ Interpretable groups in Mann pairs ⋮ Difference Algebra ⋮ A simple criterion ⋮ Tame expansions of \({\omega}\)-stable theories and definable groups

Cites Work

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• Lazard's theorem for differential algebraic groups and proalgebraic groups.
• Unidimensional theories are superstable
• Groups definable in local fields and pseudo-finite fields
• Some foundational questions concerning differential algebraic groups
• Hyperimaginaries and automorphism groups
• MODEL THEORY OF DIFFERENCE FIELDS, II: PERIODIC IDEALS AND THE TRICHOTOMY IN ALL CHARACTERISTICS
• Definability and definable groups in simple theories
• Model theory of difference fields
• Pro-algebraic and differential algebraic group structures on affine spaces

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