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TFM_Aguilar Enriquez_Miguel Alejandro.pdf (1.06 MB)

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Master thesis

Publication date

2024-09

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cc by-nc-nd (c) Aguilar Enríquez, 2024
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/215518

The mountain pass theorem on subsystems of second order arithmetic

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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.

Description

Treballs Finals del Màster de Lògica Pura i Aplicada, Facultat de Filosofia, Universitat de Barcelona. Curs: 2023-2024. Tutor: David Fernández-Duque

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Lògica matemàtica, Aritmètica, Espais de Hilbert, Espais de Banach, Treballs de fi de màster

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Mathematical logic, Arithmetic, Hilbert space, Banach spaces, Master's thesis

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Màster Oficial - Pure and Applied Logic / Lògica Pura i aplicada

Citation

AGUILAR ENRÍQUEZ, Miguel Alejandro. The mountain pass theorem on subsystems of second order arithmetic. [consulted: 14 of June of 2026]. Available at: https://hdl.handle.net/2445/215518

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