Arithmetical Soundness and Completeness for $$\varvec{\Sigma }_{\varvec{2}}$$ Numerations |
| |
Authors: | Taishi Kurahashi |
| |
Institution: | 1.Department of Natural Science,National Institute of Technology, Kisarazu College,Kisarazu,Japan |
| |
Abstract: | We prove that for each recursively axiomatized consistent extension T of Peano Arithmetic and \(n \ge 2\), there exists a \(\Sigma _2\) numeration \(\tau (u)\) of T such that the provability logic of the provability predicate \(\mathsf{Pr}_\tau (x)\) naturally constructed from \(\tau (u)\) is exactly \(\mathsf{K}+ \Box (\Box ^n p \rightarrow p) \rightarrow \Box p\). This settles Sacchetti’s problem affirmatively. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|