Omitting quantifier-free types in generic structures

DOI10.2307/2272737zbMath0273.02038OpenAlexW2000947982MaRDI QIDQ5181683

Angus J. Macintyre

Publication date: 1972

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2272737

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Applications of computability and recursion theory (03D80) Other classical first-order model theory (03C68) Metamathematical considerations in group theory (20A10)

Related Items (17)

Cototal enumeration degrees and their applications to effective mathematics ⋮ Higman's embedding theorem in a general setting and its application to existentially closed algebras ⋮ Algebraic equivalents of the solvability of group-theoretic algorithmic problems ⋮ Countable infinite existentially closed models of universally axiomatizable theories ⋮ Infinite groups ⋮ Decidable fragments of universal theories and existentially closed models ⋮ Algebraically closed groups ⋮ Satisfaction of existential theories in finitely presented groups and some embedding theorems. ⋮ Uncountable universal locally finite groups ⋮ Robinson forcing is not absolute ⋮ Model-companions and definability in existentially complete structures ⋮ Finitely determined members of varieties of groups and rings ⋮ Computably enumerable sets and quasi-reducibility ⋮ Classifying topoi and finite forcing ⋮ Model-theoretic and algorithmic questions in group theory ⋮ The word problem for division rings ⋮ More undecidable lattices of Steinitz exchange systems

Cites Work

• Existentially closed structures
• Completing theories by forcing

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