Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/135558
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Casanovas Ruiz-Fornells, Enrique | - |
dc.contributor.author | Casado Telletxea, Ioar | - |
dc.date.accessioned | 2019-06-20T07:37:33Z | - |
dc.date.available | 2019-06-20T07:37:33Z | - |
dc.date.issued | 2019-01-18 | - |
dc.identifier.uri | http://hdl.handle.net/2445/135558 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Enrique Casanovas Ruiz-Fornells | ca |
dc.description.abstract | [en] Lindström’s theorem characterizes first-order logic as the most expressive among those that satisfy the countable Compactness and downward Löwenheim-Skolem theorems. Given the importance of this results in model theory, Lindström’s theorem justifies, to some extent, the privileged position of first-order logic in contemporary mathematics. Even though Lindström’s theorem gives a negative answer to the problem of finding a proper extension of first-order logic satisfying the same model-theoretical properties, the study of these extensions has been of great importance during the second half of the XX. century: logicians were trying to find systems that kept a balance between expressive power and rich model-theoretical properties. The goal of this essay is to prove Lindström’s theorem, along with its prerequisites, and to give weaker versions of the Compactness and Löwenheim-Skolem theorems for the logic L ( Q 1 ) (first-order logic with the quantifier "there exist uncountably many"), which we present as an example of extended logic with good model-theoretical properties. | ca |
dc.format.extent | 54 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc-by-nc-nd (c) Ioar Casado Telletxea, 2019 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Lògica de primer ordre | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Teoria de models | ca |
dc.subject.other | First-order logic | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Model theory | en |
dc.title | Compactness and Löwenheim-Skolem theorems in extensions of first-order logic | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
memoria.pdf | Memòria | 350.79 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License