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A Model Theoretical Generalization of Steinitz’s Theorem

Author(s): Alexandre Martins Rodrigues | Edelcio de Souza

Journal: Principia : an International Journal of Epistemology
ISSN 1414-4247

Volume: 15;
Issue: 1;
Start page: 107;
Date: 2011;
Original page

Keywords: Strong isomorphism | infinitary languages | isomorphism extension | quantifier elimination.

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.
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