Structures coordinatized by indiscernible sets
type: Item
instance of: scholarly article
title: Structures coordinatized by indiscernible sets
zbMATH Open document ID: 0655.03020
DOI: 10.1016/0168-0072(87)90003-0
published in: Annals of Pure and Applied Logic
publication date: 1987-01-01T00:00:00Z
review text: The paper studies countable \(\aleph_ 0\)-stable, \(\aleph_ 0\)- categorical structures M which satisfy: any strictly minimal set definable in \(M^{eq}\) is indescernible. In particular, it is shown that each such structure admits a finite language and is uniformly explicitly definable from a countable linear ordering. The author conjectures that some of the results proved for this class of structures will turn out to be true for the broader class of countable \(\aleph_ 0\)-stable, \(\aleph_ 0\)-categorical structures.
Mathematics Subject Classification ID: 03C35
Mathematics Subject Classification ID: 03C45
zbMATH DE Number: 4068844
zbMATH Keywords: categoricity
zbMATH Keywords: strictly minimal set
author: Alistair H. Lachlan
reviewed by: Jörg Flum
MaRDI profile type: Publication
full work available at URL: 0168-0072(87)90003-0
OpenAlex ID: W2085423903
cites work: Quasi finitely axiomatizable totally categorical theories
cites work: \(\aleph _ 0\)-categorical, \(\aleph _ 0\)-stable structures
cites work: Stable Finitely Homogeneous Structures
cites work: Two conjectures regarding the stability of ω-categorical theories
cites work: On countable stable structures which are homogeneous for a finite relational language
cites work: Stable structures homogeneous for a finite binary language
cites work: Classification theory and the number of non-isomorphic models
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description: scientific article; zbMATH DE number 4068844