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The ∑ 1-Provability Logic of Intuitionistic Arithmetic

Mojtahedi, Mojtaba | 2011

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 45487 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Ardeshir, Mohammad
  7. Abstract:
  8. In this dissertation, we study (first-order) arithmetical interpretations for propositional (modal and non-modal) logics. More precisely, the following results are included in this dissertation: an axiomatization for provability logic of Heyting Arithmetic, HA, and its self-completion HA := HA + PrHA(⌜A⌝) ! A for 1-substitutions is provided, and their arithmetical completeness theorems are proved. We also show that they are decidable. The de Jongh property for Basic Arithmetic BA, HA and HA + □ are proved
  9. Keywords:
  10. Heyting Arithmetic ; Basic Logic ; Provability Logic ; DeJongh Property

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