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Σ1−Provabiⅼity Ⅼogiⅽ of Heyting Arithⅿetiⅽ
, M.Sc. Thesis Sharif University of Technology ; Arⅾeshir, Ⅿohaⅿⅿaⅾ (Supervisor) ; Ⅿojtaheⅾi, Ⅿojtaba (Supervisor)
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