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 (...)
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  2. Konstantin N. Ignatiev (1993). The Provability Logic for Σ1-Interpolability. Annals of Pure and Applied Logic 64 (1):1-25.
    We say that two arithmetical formulas A, B have the Σ1-interpolation property if they have an ‘interpolant’ σ, i.e., a Σ1 formula such that the formulas A→σ and σ→B are provable in Peano Arithmetic PA. The Σ1-interpolability predicate is just a formalization of this property in the language of arithmetic.Using a standard idea of Gödel, we can associate with this predicate its provability logic, which is the set of all formulas that express arithmetically valid principles in the modal language with (...)
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  3. Konstantin N. Ignatiev (1993). The Provability Logic for Σ< Sub> 1-Interpolability. Annals of Pure and Applied Logic 64 (1):1-25.
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