Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/215518
Title: The mountain pass theorem on subsystems of second order arithmetic
Author: Aguilar Enríquez, Miguel Alejandro
Director/Tutor: Fernández Duque, David
Keywords: Lògica matemàtica
Aritmètica
Espais de Hilbert
Espais de Banach
Treballs de fi de màster
Mathematical logic
Arithmetic
Hilbert space
Banach spaces
Master's thesis
Issue Date: Sep-2024
Abstract: The main goal of this work is to formalize the Mountain Pass Theorem of Ambrosetti and Rabinowitz within the formal subsystem of second order arithmetic known as ACA0. We develop some Analysis within this system to have access to the space of continuous functions from [0, 1] into a separable Banach space and from there built formalized proofs of the basic ingredients of the Mountain Pass Theorem: The deformation lemma and the minimax principle that proves the theorem itself.
Note: Treballs Finals del Màster de Lògica Pura i Aplicada, Facultat de Filosofia, Universitat de Barcelona. Curs: 2023-2024. Tutor: David Fernández-Duque
URI: http://hdl.handle.net/2445/215518
Appears in Collections:Màster Oficial - Pure and Applied Logic / Lògica Pura i aplicada

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