A Model Theoretical Generalization of Steinitz’s Theorem

Alexandre Martins Rodrigues, Edelcio de Souza


Infinitary languages are used to prove that any strong isomorphism of substructures of isomorphic structures can be extended to an isomorphism of the structures. If the structures are models of a theory that has quantifier elimination, any isomorphism of substructures is strong. This theorem is a partial generalization of Steinitz’s theorem for algebraically closed fields and has as special case the analogous theorem for differentially closed fields. In this note, we announce results which will be proved elsewhere.


Strong isomorphism; infinitary languages; isomorphism extension; quantifier elimination.

DOI: https://doi.org/10.5007/1808-1711.2011v15n1p107

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Principia: an internationnal journal of epistemology
Published by NEL - Epistemology and Logic Research Group
Federal University of Santa Catarina - UFSC
Center of Philosophy and Human Sciences – CFH
Campus Reitor João David Ferreira Lima
Florianópolis, Santa Catarina - Brazil
CEP: 88040-900

 ISSN: 1414-4217
EISSN: 1808-171

e-mail: principia@contato.ufsc.br