First order theory of permutation groups

DOI10.1007/BF02762670zbMath0284.20003OpenAlexW2034715072MaRDI QIDQ1845064

Saharon Shelah

Publication date: 1973

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

Full work available at URL: https://doi.org/10.1007/bf02762670

Mathematics Subject Classification ID

Free nonabelian groups (20E05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Axiomatics and elementary properties of groups (20A05) General theory for finite permutation groups (20B05) Metamathematical considerations in group theory (20A10)

Related Items

Unnamed Item, Permutations and implicit definability, On the automorphism groups of homogeneous and saturated Boolean algebras, Recognizing the Real Line, Embeddings in groups of permutations with supports of bounded cardinality, Some Universal Sets of Terms, The automorphism tower problem revisited, Elementary equivalent pairs of algebras associated with sets, There are just four second-order quantifiers, Ultraproducts and elementary types of some groups related to infinite symmetric groups, On the elementary equivalence of automorphism groups of Boolean algebras; downward Skolem Löwenheim theorems and compactness of related quantifiers, Elementary definability of symmetry groups, Rigid homogeneous chains, On the reconstruction of boolean algebras from their automorphism groups, Errata to: First order theory of permutation groups, On distinguishing quotients of symmetric groups, Elementary equivalence of infinite-dimensional classical groups

Cites Work

• There are just four second-order quantifiers
• On elementary types of symmetric groups
• The first order properties of products of algebraic systems
• Partition relations for cardinal numbers
• Intersection Theorems for Systems of Sets (II)
• On definability of ordinals in logic with infinitely long expressions
• Decidability of Second-Order Theories and Automata on Infinite Trees
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