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The Σ1-Provability Logic of HA

Ardeshir, M ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1017/jsl.2019.44
  3. Publisher: Cambridge University Press , 2019
  4. Abstract:
  5. For the Heyting Arithmetic HA,HA is defined [14, 15] as the theory {A | HA-A}, where is called the box translation of A (Definition 2.4). We characterize the Σ1-provability logic of HA as a modal theory (Definition 3.17). © 2019 The Association for Symbolic Logic
  6. Keywords:
  7. Completeness principle ; Heyting arithmetic ; Intuitionistic logic ; Modal logic ; Provability logic
  8. Source: Journal of Symbolic Logic ; Volume 84, Issue 3 , 2019 , Pages 1118-1135 ; 00224812 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0168007218300617