Model completeness for trivial, uncountably categorical theories of Morley rank \(1\)
type: Item
instance of: scholarly article
title: Model completeness for trivial, uncountably categorical theories of Morley rank \(1\)
zbMATH Open document ID: 1111.03035
author: Alfred Dolich
author: Alexander Raichev
author: M. C. Laskowski
published in: Archive for Mathematical Logic
publication date: 2007-01-24T00:00:00Z
review text: The main theorem: If \(T\) is a trivial uncountably categorical theory of Morley rank 1, then the theory obtained from \(T\) by naming constants for a model is model complete. This result is in some senses optimal. There exist trivial Morley rank 1 theories which are not categorical and for which the conclusion of the theorem fails. Also, \textit{D. Marker} [``Non \(\Sigma_n\) axiomatizable almost strongly minimal theories'', J. Symb. Log. 54, 921--927 (1989; Zbl 0698.03021)] constructed trivial totally categorical theories of Morley rank 2 which are not model complete after naming any set of constants.
Mathematics Subject Classification ID: 03C10
Mathematics Subject Classification ID: 03C35
zbMATH DE Number: 5118081
zbMATH Keywords: categorical theories
zbMATH Keywords: Morley rank
zbMATH Keywords: model completeness
MaRDI profile type: Publication
full work available at URL: s00153-006-0019-x
OpenAlex ID: W2089558857
cites work: Q4889877
cites work: Trivial, strongly minimal theories are model complete after naming constants
cites work: Non Σn axiomatizable almost strongly minimal theories
cites work: Q3130253
DOI: 10.1007/S00153-006-0019-X
description: scientific article; zbMATH DE number 5118081