Model Theoretical Generalization of Steinitz’s Theorem DOI: 10.5007/1808-1711.2011v15n1p107
Alexandre Martins Rodrigues, Edelcio Gonçalves de Souza · Principia an international journal of epistemology · 2011
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.