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Provability Logic

Aboolian, Narbe | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44075 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Behrostaghi, Mohammad Ardeshir
  7. Abstract:
  8. 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
  9. Keywords:
  10. Modal Logic ; Provability ; Peano Arithmetic

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