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Elimination of cut-type rules from the Robinson and Presburger axiomatic systems

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Literature cited

  1. 1.

    A. Yu. Plyushkevichene, “Specialization of the use of axioms for deduction search in axiomatic theories with equality,” Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR,20, 175–185 (1971).

  2. 2.

    A. Yu. Plyushkevichene, “Elimination of cut-type rules in axiomatic theories with equality,” Seminars in Mathematics, Vol. 16, Consultants Bureau, New York (1971), pp. 90–94.

  3. 3.

    M. T. Rogava, “On sequential modifications of applied predicate calculi,” Seminars in Mathematics, Vol. 4, Consultants Bureau, New York (1969), pp. 77–81.

  4. 4.

    S. C. Kleene, “Permutability of inferences in Gentzen's calculi LK and LJ,” Mem. Amer. Math. Soc., No. 10, pp. 1–26 (1952).

  5. 5.

    M. Presburger, “Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchen die Addition als einzige Operation hervortritt,” Compt. Rend. I Congr. Mathematiciens des Pays Slaves, Warsaw (1930), pp. 92–101; 395.

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Additional information

The principal results of this article were reported at the Leningrad Seminar on Mathematical Logic on May 19, 1970.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 20, pp. 186–199, 1971.

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Plyushkevichene, A.Y. Elimination of cut-type rules from the Robinson and Presburger axiomatic systems. J Math Sci 1, 117–125 (1973). https://doi.org/10.1007/BF01117478

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Keywords

  • Axiomatic System