Läuchli's completeness theorem from a topos-theoretic perspective
We prove a variant of Läuchli's completeness theorem for intuitionistic predicate calculus. The formulation of the result relies on the observation (due to Lawvere) that Läuchli's theorem is related to the logic of the canonical indexing of the atomic topos of ℤ-sets. We show that the proc...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/120204 |
| Acceso en línea: | http://hdl.handle.net/11336/120204 |
| Access Level: | acceso abierto |
| Palabra clave: | LÄUCHLI'S COMPLETENESS THEOREM TOPOS THEORY https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We prove a variant of Läuchli's completeness theorem for intuitionistic predicate calculus. The formulation of the result relies on the observation (due to Lawvere) that Läuchli's theorem is related to the logic of the canonical indexing of the atomic topos of ℤ-sets. We show that the process that transforms Kripke-counter-models into Läuchli-counter-models is (essentially) the inverse image of a geometric morphism. Completeness follows because this geometric morphism is an open surjection. |
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