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Title: Compactness and Löwenheim-Skolem theorems in extensions of first-order logic
Author: Casado Telletxea, Ioar
Director/Tutor: Casanovas Ruiz-Fornells, Enrique
Keywords: Lògica de primer ordre
Treballs de fi de grau
Teoria de models
First-order logic
Bachelor's thesis
Model theory
Issue Date: 18-Jan-2019
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.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Enrique Casanovas Ruiz-Fornells
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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