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The Σ1-provability logic of HA

Ardeshir, M ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1016/j.apal.2018.05.001
  3. Publisher: Elsevier B.V , 2018
  4. Abstract:
  5. In this paper we introduce a modal theory iHσ which is sound and complete for arithmetical Σ1-interpretations in HA, in other words, we will show that iHσ is the Σ1-provability logic of HA. Moreover we will show that iHσ is decidable. As a by-product of these results, we show that HA+□⊥ has de Jongh property. © 2018 Elsevier B.V
  6. Keywords:
  7. Heyting Arithmetic ; Intuitionistic logic ; Modal Logic ; Provability Logic
  8. Source: Annals of Pure and Applied Logic ; Volume 169, Issue 10 , 2018 , Pages 997-1043 ; 01680072 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0168007218300617