The mountain pass theorem on subsystems of second order arithmetic

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.

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

Country

Spain

Related Organizations

University of Barcelona
Spain

Keywords

Lògica matemàtica, Banach spaces, Arithmetic, Espais de Hilbert, Mathematical logic, Aritmètica, Hilbert space, Espais de Banach, Master's thesis, Treballs de fi de màster

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