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 |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
TFM_Aguilar Enriquez_Miguel Alejandro.pdf | 1.08 MB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License