Σ1−Provabiⅼity Ⅼogiⅽ of Heyting Arithⅿetiⅽ

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Ⅾejborⅾ, Naviⅾ | 2024

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 58315 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Arⅾeshir, Ⅿohaⅿⅿaⅾ; Ⅿojtaheⅾi, Ⅿojtaba
Abstract:
In this thesis we will study the Σ1-provability logic of HA; to be more precise, we will review logico-mathematical preliminaries from branches such as modal logic, arithmetical theories, constructive mathematics, etc, and finally show that iHσ is a modal theory that is sound and complete for arithmetical Σ1-interpretations in HA and it is decidable
Keywords:
Provability Logic ; Intuitionism ; Arithmetic ; Modal Logic ; Interpretability ; Realizability