A Model Theoretical Generalization of Steinitz’s Theorem
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 pa...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Universidade Federal de Santa Catarina
2011-04-01
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| Series: | Principia: An International Journal of Epistemology |
| Subjects: | |
| Online Access: | http://www.periodicos.ufsc.br/index.php/principia/article/view/1808-1711.2011v15n1p107/20556 |
| _version_ | 1811297994615554048 |
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| author | Alexandre Martins Rodrigues Edelcio de Souza |
| author_facet | Alexandre Martins Rodrigues Edelcio de Souza |
| author_sort | Alexandre Martins Rodrigues |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T06:12:26Z |
| format | Article |
| id | doaj.art-2f0d37ded6304041bba217aad56e86f7 |
| institution | Directory Open Access Journal |
| issn | 1414-4247 1808-1711 |
| language | English |
| last_indexed | 2024-04-13T06:12:26Z |
| publishDate | 2011-04-01 |
| publisher | Universidade Federal de Santa Catarina |
| record_format | Article |
| series | Principia: An International Journal of Epistemology |
| spelling | doaj.art-2f0d37ded6304041bba217aad56e86f72022-12-22T02:58:57ZengUniversidade Federal de Santa CatarinaPrincipia: An International Journal of Epistemology1414-42471808-17112011-04-01151107110A Model Theoretical Generalization of Steinitz’s TheoremAlexandre Martins RodriguesEdelcio de SouzaInfinitary 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.http://www.periodicos.ufsc.br/index.php/principia/article/view/1808-1711.2011v15n1p107/20556Strong isomorphisminfinitary languagesisomorphism extensionquantifier elimination. |
| spellingShingle | Alexandre Martins Rodrigues Edelcio de Souza A Model Theoretical Generalization of Steinitz’s Theorem Principia: An International Journal of Epistemology Strong isomorphism infinitary languages isomorphism extension quantifier elimination. |
| title | A Model Theoretical Generalization of Steinitz’s Theorem |
| title_full | A Model Theoretical Generalization of Steinitz’s Theorem |
| title_fullStr | A Model Theoretical Generalization of Steinitz’s Theorem |
| title_full_unstemmed | A Model Theoretical Generalization of Steinitz’s Theorem |
| title_short | A Model Theoretical Generalization of Steinitz’s Theorem |
| title_sort | model theoretical generalization of steinitz s theorem |
| topic | Strong isomorphism infinitary languages isomorphism extension quantifier elimination. |
| url | http://www.periodicos.ufsc.br/index.php/principia/article/view/1808-1711.2011v15n1p107/20556 |
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