S. Buss, The modal logic of pure provability, Notre Dame Journal of Formal Logic, vol. 31 (1990), no. 2, pp. 225--231.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....order logic of formal provability was not axiomatizable. The issue of provability semantics for S4 was addressed by Lemmon [65] Myhill [77] 78] Kripke [58] Montague [76] Novikov [79] Mints [73] Kuznetsov and Muravitsky [63] Goldblatt [42] Boolos [25] 26] Shapiro [88] 89] Buss [29], Artemov [5] and many others. However, there were no adequate Godelian provability semantics for S4 found 5 . Moreover, in [76] the problem was announced hopeless. In this paper we give a complete solution to the problem of provability semantics for S4 (Problem 1 above) as it was understood ....

S. Buss, The modal logic of pure provability, Notre Dame Journal of Formal Logic, vol. 31 (1990), no. 2, pp. 225--231.

....theorem. In [26] cf. 59] Godel again acknowledged the problem of the provability semantics for S4. This issue was also addressed by Lemmon [44] Myhill [55] 56] Kripke [40] Montague [54] Mints [52] Kuznetsov Muravitsky [43] Goldblatt [27] Boolos [12] 14] Shapiro [62] 63] Buss [17], Artemov [1] and many others. However, the problem of finding an adequate provability semantics for S4 has remained open. A principal difficulty here is caused by the existential quantifier over proofs in the provability formula Provable(y) which is 9xProof (x; y) where Proof (x; y) is the ....

S. Buss, "The Modal Logic of Pure Provability", Notre Dame Journal of Formal Logic, v. 31, No. 2, 1990

....provable in PA, which contradicts the Second Godel Incompleteness Theorem. The issue of a provability model for S4 was studied by Godel [18] Lemmon [29] Myhill [39] 40] Kripke [26] Montague [38] Mints [35] Kuznetsov Muravitskii [28] Goldblatt [19] Boolos [9] 10] Shapiro [43] 44] Buss [12], Artemov [1] and many others. However, the problem of a formal provability semantics for S4 has remained open. A principal difficulty here is caused by the existential quantifier over proofs in Provable(F ) Indeed, the interpretation of the formula 2(2F F ) is it is provable that Provable(F ....

S. Buss, "The Modal Logic of Pure Provability", Notre Dame Journal of Formal Logic, v. 31, No. 2, 1990

....provable in PA, which contradicts the Second Godel Incompleteness Theorem. The issue of a provability model for S4 was studied by Godel [13] Lemmon [20] Myhill [27] 28] Kripke [18] Montague [26] Mints [25] Kuznetsov Muravitskii [19] Goldblatt [14] Boolos [7] 8] Shapiro [30] 31] Buss [9], Artemov [1] and many others. However, the problem of a formal provability semantics for S4 has remained open. A principal difficulty here is caused by the existential quantifier over proofs in Provable(F ) Indeed, the interpretation of the formula 2(2F F ) is it is provable that Provable(F ....

S. Buss, "The Modal Logic of Pure Provability", Notre Dame Journal of Formal Logic, v. 31, No. 2, 1990

....provable in PA, which contradicts the second Godel incompleteness theorem. The issue of a provability model for S4 was studied by Godel [16] Lemmon [28] Myhill [35] 36] Kripke [25] Montague [34] Mints [33] Kuznetsov Muravitskii [27] Goldblatt [17] Boolos [9] 10] Shapiro [38] 39] Buss [11], Artemov [1] and many others. However, the problem of a formal provability semantics for S4 has remained open. A principal difficulty here is caused by the existential quantifier over proofs in Provable(F ) Indeed, the interpretation of the formula 2(2F F ) is it is provable that Provable(F ....

S. Buss, "The Modal Logic of Pure Provability", Notre Dame Journal of Formal Logic, v. 31, No. 2, 1990

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S. Buss, The modal logic of pure provability, Notre Dame Journal of Formal Logic, vol. 31 (1990), no. 2, pp. 225--231.

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