1. Konstantin N. Ignatiev (1993). On Strong Provability Predicates and the Associated Modal Logics. Journal of Symbolic Logic 58 (1):249-290.
    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 (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  2. Konstantin N. Ignatiev (1993). The Provability Logic for Σ1-Interpolability. Annals of Pure and Applied Logic 64 (1):1-25.
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  3. Konstantin N. Ignatiev (1993). The Provability Logic for Σ< Sub> 1-Interpolability. Annals of Pure and Applied Logic 64 (1):1-25.
    Direct download  
     
    My bibliography  
     
    Export citation