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 |
| Sumario: | [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. |
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