Refuting Ehrenfeucht conjecture on rigid models
type: Item
instance of: scholarly article
title: Refuting Ehrenfeucht conjecture on rigid models
zbMATH Open document ID: 0359.02053
DOI: 10.1007/BF02757005
author: S. Shelah
published in: Israel Journal of Mathematics
publication date: 1976-01-01T00:00:00Z
review text: A. Ehrenfeucht conjectured that for countable first order theories \(T\) the set \(RS(T)=\{\lambda:T\) has a rigid model of cardinality \(\lambda\}\) is always convex, its lower bound is \(\omega\) or \(\omega_1\) and its upper bound \(\infty\) or smaller than \(\beth_{\omega_1}\). In the paper it is proved that for any \(\Sigma_2\)-sentence \(\chi\) of pure second order logic there is a first order sentence \(\psi\) such that \(RS(\psi)=\{\lambda:\lambda=\omega\) or \(\sum\limits_{\varkappa<\lambda}\varkappa^\omega=\lambda\) and \(\lambda\models\chi\}\). Thus Ehrenfeucht's conjecture is disproved.
Mathematics Subject Classification ID: 03C68
zbMATH DE Number: 3559564
Wikidata QID: Q122931580
MaRDI profile type: Publication
cites work: Model theory
cites work: Q5546782
cites work: One hundred and two problems in mathematical logic
cites work: Complete theories with countably many rigid nonisomorphic models
cites work: Q4078077
cites work: Categoricity in Power
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description: scientific article; zbMATH DE number 3559564