\({\mathcal M}\)-gap conjecture and \(m\)-normal theories

DOI10.1007/BF02773473zbMath0914.03040WikidataQ122945548 ScholiaQ122945548MaRDI QIDQ1269775

Ludomir Newelski

Publication date: 21 June 1999

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

stable theorysuperstable theorycountable models\(m\)-independence\({\mathcal M}\)-gap conjecture\({\mathcal M}\)-rank\(*\)-algebraic element\(*\)-finite tuples\(m\)-normal theorygeneric subgroupindependence induced by measureisolated generic typemeasure independencesmall weakly minimal groupsstationarizations of typestraces of typestype-definable group

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Structure and classification of infinite or finite groups (20E99) Classification theory, stability, and related concepts in model theory (03C45) Models with special properties (saturated, rigid, etc.) (03C50) Models of other mathematical theories (03C65)

Related Items (11)

Small profinite groups and rings ⋮ Geometric stability theory for \(\mu\)-structures ⋮ DEFINABLE TOPOLOGICAL DYNAMICS ⋮ Small profinite groups ⋮ Some model theory of Polish structures ⋮ Small profinite structures ⋮ Products of finite abelian groups as profinite groups ⋮ Profinite structures interpretable in fields ⋮ Geometry of *-Finite Types ⋮ Generalizations of small profinite structures ⋮ Vaught's conjecture for some meager groups

Cites Work

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• A survey of basic stability theory, with particular emphasis on orthogonality and regular types
• A proof of Vaught's conjecture for \(\omega\)-stable theories
• Superstable groups
• On type definable subgroups of a stable group
• Classification theory and the number of non-isomorphic models.
• Meager forking
• Forcing isomorphism II
• A proof of Saffe's conjecture
• The classification of small weakly minimal sets. II
• A model and its subset
• ℳ-rank and meager types
• On atomic or saturated sets
• Geometry of *-Finite Types

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