# name
Compactness and Löwenheim-Skolem theorems in extensions of first-order logic

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Enrique Casanovas Ruiz-Fornells

# metadata.dc.description.abstract[].value
[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.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Ioar Casado Telletxea, 2019

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Compactness and Löwenheim-Skolem theorems in extensions of first-order logic