Contributions to the model theory of equality-free logic
[eng] This thesis is a study of the theory of models of logic without identity. The fragment of first-order logic composed of formulas that do not have the identity symbol is studied. The fundamental concepts studied are that of "Leibniz's congruence" and that of "Relative Relati...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 1996 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:dnet:ubarcelona__::f94c8742d27eb654185d8bdd3d1064de |
| Acceso en línea: | https://hdl.handle.net/2445/228548 https://hdl.handle.net/10803/697157 |
| Access Level: | acceso abierto |
| Palabra clave: | Lògica Teoria de models Logic Model theory info:eu-repo/semantics/publishedVersion |
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Contributions to the model theory of equality-free logicDellunde i Clavé, PilarLògicaTeoria de modelsLogicModel theoryinfo:eu-repo/semantics/publishedVersion[eng] This thesis is a study of the theory of models of logic without identity. The fragment of first-order logic composed of formulas that do not have the identity symbol is studied. The fundamental concepts studied are that of "Leibniz's congruence" and that of "Relative Relation". The current interest in these notions comes from the works of W. Blok and D. Pigozzi. We have studied this logic from the point of view of classical model theory, developing common techniques in model theory: diagram method, Back-And-Forth systems, etc. in order to obtain algebraic characterizations of elementary equivalence in this logic and preservation theorems. One of the most important contributions of this work is the characterization of first-order statements that are logically equivalent to a statement without identity. We have introduced the notions of a saturated, universal and homogeneous model without identity and we have studied their properties and compared them with those of analogous notions in first-order logic with identity. Finally, we have studied Horn's universal fragment without identity of the infinite languages, with regular infinite cardinal "ands". We have obtained characterization and preservation results; Using these results we have proved interpolation and definability theorems for this fragment.[spa] La presente tesis es un estudio de la teoría de modelos de la lógica sin identidad. Se estudia el fragmento de la lógica de primer orden compuesto por las fórmulas que no tienen el símbolo de identidad. Los conceptos fundamentales estudiados son el de "congruencia de Leibniz" y el de "relación de parentesco (Relative Relation)". El interés actual de estas nociones procede de los trabajos de W. Blok y de D. Pigozzi. Hemos estudiado esta lógica desde el punto de vista de la teoría de modelos clásica, desarrollando técnicas usuales en teoría de modelos: método de los diagramas, sistemas de Back-And-Forth, etc. con el fin de obtener caracterizaciones algebraicas de la equivalencia elemental en esta lógica y teoremas de preservación. Una de las contribuciones más importantes de este trabajo es la caracterización de los enunciados de primer orden que son lógicamente equivalentes a un enunciado sin identidad. Hemos introducido las nociones de modelo saturado, universal y homogéneo sin identidad y hemos estudiado sus propiedades y las hemos comparado con las de las nociones análogas en lógica de primer orden con identidad. Finalmente hemos estudiado el fragmento universal de Horn sin identidad de los lenguajes infinitario , con “y” cardinales infinitos regulares. Hemos obtenido resultados de caracterización y de preservación; usando estos resultados hemos demostrado teoremas de interpolación y definibilidad para este fragmento.Universitat de BarcelonaJansana, RamonUniversitat de Barcelona. Departament de Lògica, Història i Filosofia de la Ciència1996info:eu-repo/semantics/doctoralThesisapplication/pdfhttps://hdl.handle.net/2445/228548https://hdl.handle.net/10803/697157Tesis Doctorals - Departament - Lògica, Història i Filosofia de la Ciènciareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc by-nc (c) Dellunde i Clavé, Pilar, 1996http://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessoai:dnet:ubarcelona__::f94c8742d27eb654185d8bdd3d1064de2026-05-27T06:46:51Z |
| dc.title.none.fl_str_mv |
Contributions to the model theory of equality-free logic |
| title |
Contributions to the model theory of equality-free logic |
| spellingShingle |
Contributions to the model theory of equality-free logic Dellunde i Clavé, Pilar Lògica Teoria de models Logic Model theory info:eu-repo/semantics/publishedVersion |
| title_short |
Contributions to the model theory of equality-free logic |
| title_full |
Contributions to the model theory of equality-free logic |
| title_fullStr |
Contributions to the model theory of equality-free logic |
| title_full_unstemmed |
Contributions to the model theory of equality-free logic |
| title_sort |
Contributions to the model theory of equality-free logic |
| dc.creator.none.fl_str_mv |
Dellunde i Clavé, Pilar |
| author |
Dellunde i Clavé, Pilar |
| author_facet |
Dellunde i Clavé, Pilar |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Jansana, Ramon Universitat de Barcelona. Departament de Lògica, Història i Filosofia de la Ciència |
| dc.subject.none.fl_str_mv |
Lògica Teoria de models Logic Model theory info:eu-repo/semantics/publishedVersion |
| topic |
Lògica Teoria de models Logic Model theory info:eu-repo/semantics/publishedVersion |
| description |
[eng] This thesis is a study of the theory of models of logic without identity. The fragment of first-order logic composed of formulas that do not have the identity symbol is studied. The fundamental concepts studied are that of "Leibniz's congruence" and that of "Relative Relation". The current interest in these notions comes from the works of W. Blok and D. Pigozzi. We have studied this logic from the point of view of classical model theory, developing common techniques in model theory: diagram method, Back-And-Forth systems, etc. in order to obtain algebraic characterizations of elementary equivalence in this logic and preservation theorems. One of the most important contributions of this work is the characterization of first-order statements that are logically equivalent to a statement without identity. We have introduced the notions of a saturated, universal and homogeneous model without identity and we have studied their properties and compared them with those of analogous notions in first-order logic with identity. Finally, we have studied Horn's universal fragment without identity of the infinite languages, with regular infinite cardinal "ands". We have obtained characterization and preservation results; Using these results we have proved interpolation and definability theorems for this fragment. |
| publishDate |
1996 |
| dc.date.none.fl_str_mv |
1996 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/228548 https://hdl.handle.net/10803/697157 |
| url |
https://hdl.handle.net/2445/228548 https://hdl.handle.net/10803/697157 |
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Inglés |
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Inglés |
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cc by-nc (c) Dellunde i Clavé, Pilar, 1996 http://creativecommons.org/licenses/by-nc/4.0/ info:eu-repo/semantics/openAccess |
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cc by-nc (c) Dellunde i Clavé, Pilar, 1996 http://creativecommons.org/licenses/by-nc/4.0/ |
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openAccess |
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application/pdf |
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Universitat de Barcelona |
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Universitat de Barcelona |
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Tesis Doctorals - Departament - Lògica, Història i Filosofia de la Ciència reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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1869423670325149696 |
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15,811543 |