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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 44075 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Behrostaghi, Mohammad Ardeshir
- 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
- Keywords:
- Modal Logic ; Provability ; Peano Arithmetic
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