Casanovas Ruiz-Fornells, EnriqueCasado Telletxea, Ioar2019-06-202019-06-202019-01-18https://hdl.handle.net/2445/135558Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Enrique Casanovas Ruiz-Fornells[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.54 p.application/pdfengcc-by-nc-nd (c) Ioar Casado Telletxea, 2019http://creativecommons.org/licenses/by-nc-nd/3.0/es/Lògica de primer ordreTreballs de fi de grauTeoria de modelsFirst-order logicBachelor's thesesModel theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess