Hilbert’s Program

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Hosseini, Mohammad Erfan | 2023

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 56405 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Ardeshir, Mohammad
Abstract:
In this thesis, we provide a comprehensive overview of the efforts made towards achieving the goals of Hilbert’s program, and evaluate how successful They are. We begin by discussing Gödel’s incompleteness theorems, and then as a first attempt we present a brief presentation of Gentzen’s consistency theorem. Subsequently, various research fields that branched out from these initial efforts are explored, encompassing the application of the Omega-Rule, reverse mathematics, and self-verifying systems. Furthermore, we present the concept of “Almost Finitistic Consistency” as an alternative approach within Hilbert’s program. In conclusion, a thorough assessment of the success of Hilbert’s program is presented
Keywords:
Hilbert Program ; Consistency ; Omega-Rule ; Almost Finitistic Consistency ; Reverse Mathematics ; Self-Verifying Systems

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