Mathematical Object and Logical Form in Homotopy Type Theory

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Haji Mohammadzadeh, Mohammad Aref | 2024

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 57091 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Ardeshir, Mohammad
Abstract:
Arising from the intersection of two modern ideas in logic and mathematics, namely Type Theory - specifically Martin-Löf’s intuitionistic type theory, and Homotopy Theory, Homotopy Type Theory has introduced a novel formalism that formalizes every mathematical object - including constructions, definitions, and proofs - in a specific and fundamentally different way from other interpretive frameworks (such as set theory), bringing forth new results - both philosophically and mathematically. The first goal of this research is to understand the meaning of Homotopy Type Theory as a foundation for mathematics through exploring this new formalism. The second goal of this research is to understand how this theory defines different logical concepts and provides a new approach to dealing with logical principles
Keywords:
Homotopy Theory ; Intuitionistic Type Theory ; Mathematics Univalent Foundation ; Homotopy Type Theory