Provability Logic, M.Sc. Thesis Sharif University of Technology ; Behrostaghi, Mohammad Ardeshir (Supervisor)
Abstract
Provability Logic is the study of Peano Arithmetic from the point of provability. The ◻ of modal logic is interpreted as ”Provable in PA ”. Gödel’s technique of proof, in his incompleteness theorems, showed that meta-lingual sentences such as ”A is provable in PA ” can be expressed by sentences of object language. Studying provability in the system K4 will lead us to a soundness theorem but in 1976, Robert Solovay showed that if we add an axiom -known as Löb’s axiom- to the system K4, we will have a completeness theorem as well. So GL = K4 + Löb is the provability logic of PA. In this thesis we will study these theorems
Cataloging briefProvability Logic, M.Sc. Thesis Sharif University of Technology ; Behrostaghi, Mohammad Ardeshir (Supervisor)
Abstract
Provability Logic is the study of Peano Arithmetic from the point of provability. The ◻ of modal logic is interpreted as ”Provable in PA ”. Gödel’s technique of proof, in his incompleteness theorems, showed that meta-lingual sentences such as ”A is provable in PA ” can be expressed by sentences of object language. Studying provability in the system K4 will lead us to a soundness theorem but in 1976, Robert Solovay showed that if we add an axiom -known as Löb’s axiom- to the system K4, we will have a completeness theorem as well. So GL = K4 + Löb is the provability logic of PA. In this thesis we will study these theorems
Find in contentBookmark |
|