On strong provability predicates and the associated modal logics
Journal of Symbolic Logic 58 (1):249-290 (1993)
| Abstract | PA is Peano Arithmetic. Pr(x) is the usual Σ1-formula representing provability in PA. A strong provability predicate is a formula which has the same properties as Pr(·) but is not Σ1. An example: Q is ω-provable if PA + ¬ Q is ω-inconsistent (Boolos [4]). In [5] Dzhaparidze introduced a joint provability logic for iterated ω-provability and obtained its arithmetical completeness. In this paper we prove some further modal properties of Dzhaparidze's logic, e.g., the fixed point property and the Craig interpolation lemma. We also consider other examples of the strong provability predicates and their applications | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,653 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesPaolo Gentilini (1999). Proof-Theoretic Modal PA-Completeness II: The Syntactic Countermodel. Studia Logica 63 (2):245-268.
Lev D. Beklemishev (1996). Bimodal Logics for Extensions of Arithmetical Theories. Journal of Symbolic Logic 61 (1):91-124.
Sergei Artëmov & Franco Montagna (1994). On First-Order Theories with Provability Operator. Journal of Symbolic Logic 59 (4):1139-1153.
Sergei N. Artemov (2001). Explicit Provability and Constructive Semantics. Bulletin of Symbolic Logic 7 (1):1-36.
L. D. Beklemishev (1991). Provability Logics for Natural Turing Progressions of Arithmetical Theories. Studia Logica 50 (1):107 - 128.
Giorgie Dzhaparidze (1990). Decidable and Enumerable Predicate Logics of Provability. Studia Logica 49 (1):7 - 21.
Giorgie Dzhaparidze (1991). Predicate Provability Logic with Non-Modalized Quantifiers. Studia Logica 50 (1):149 - 160.
Sergei Artemov & Giorgie Dzhaparidze (1990). Finite Kripke Models and Predicate Logics of Provability. Journal of Symbolic Logic 55 (3):1090-1098.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads9 ( #113,941 of 548,984 )Recent downloads (6 months)1 ( #63,327 of 548,984 )How can I increase my downloads? |
My notes
Discussion
