Provability logic and the completeness principle |
| |
Authors: | Albert Visser Jetze Zoethout |
| |
Institution: | 1. Philosophy, Faculty of Humanities, Utrecht University, Janskerkhof 13, 3512BL Utrecht, the Netherlands;2. Mathematical Institute, Faculty of Science, Utrecht University, Budapestlaan 6, 3584CD Utrecht, the Netherlands |
| |
Abstract: | The logic is the intuitionistic version of Löb's Logic plus the completeness principle . In this paper, we prove an arithmetical completeness theorems for for theories equipped with two provability predicates □ and △ that prove the schemes and for . We provide two salient instances of the theorem. In the first, □ is fast provability and △ is ordinary provability and, in the second, □ is ordinary provability and △ is slow provability.Using the second instance, we reprove a theorem previously obtained by Mohammad Ardeshir and Mojtaba Mojtahedi 1] determining the -provability logic of Heyting Arithmetic. |
| |
Keywords: | 03F45 03F50 03F55 Provability logic Constructivism |
本文献已被 ScienceDirect 等数据库收录! |
|