J. Myhill, Some remarks on the notion of proof, Journal of Philosophy, vol. 57 (1960), pp. 461--471.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the modal logic L 4 axiomatized all propositional properties of the formal provability, and by Artemov [4] and Vardanyan [102] who demonstrated that the first 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 ....

J. Myhill, Some remarks on the notion of proof, Journal of Philosophy, vol. 57 (1960), pp. 461--471.

....The latter formula expresses the assertion that Consis PA is provable in PA, which is false according to the second Godel incompleteness 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 ....

J. Myhill, "Some Remarks on the Notion of Proof", Journal of Philosophy, 57, pp. 461471, 1960

....expressing the consistency of PA. By necessitation, S4 derives 2(2F F ) The latter formula expresses the assertion that Consis PA is 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 ....

J. Myhill, "Some Remarks on the Notion of Proof", Journal of Philosophy, 57, pp. 461471, 1960

....expressing the consistency of PA. By necessitation, S4 derives 2(2F F ) The latter formula expresses the assertion that Consis PA is 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 ....

J. Myhill, "Some Remarks on the Notion of Proof ", Journal of Philosophy, 57, pp. 461471, 1960

....expressing the consistency of PA. By necessitation, S4 derives 2(2 ) The latter formula expresses the assertion that Consis PA is 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 ....

J. Myhill, "Some Remarks on the Notion of Proof ", Journal of Philosophy, 57, pp. 461471, 1960

No context found.

J. Myhill, Some remarks on the notion of proof, Journal of Philosophy, vol. 57 (1960), pp. 461--471.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC