Abstract
After the discovery of the arithmetical hierarchy Mostowski realized that there are further general recursion-theoretic facts which lie in the foundation of the incompleteness theorems and related results. In his articles (see Mostowski, 1979) he has made attempts to investigate formal systems from the recursion-theoretic point of view. Particularly, he has shown that the restriction to recursively enumerable systems is irrelevant for the 1st incompleteness theorem.
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References and Related Works
Boolos, G., 1976, On Deciding the Truth of Certain Fixed Point Statements Involving the Notion of Consistency, J.S.L., 41:177–178.
Boolos, G., 1977, On Deciding the Provability of Certain Fixed Point Statements, J.S.L., 42:191–193.
Davis, M., 1965, “The Undecidable,” Raven Press, New York.
Erchov, Y. L., 1980, “The Undecidability Problems and Constructive Models,” Nauka, Moscow (in Russian).
Feferman, S., 1960, Arithmetization of Metamathematics in General Setting, Fund.Math., 49:35–92.
Feferman, S., 1962, Transfinite Recursive Progression of Axiomatic Theories, J.S.L., 27:259–316.
Kleene, S. C., 1952, “Introduction to Metamathematics,” North-HoHand, Amsterdam.
Kreisel, G., 1962, On Weak Completeness of Intuitionistic Predicate Logic, J.S.L., 27:139–158.
Kreisel, G., and Takeuti, G., 1974, Formally Self-referential Propositions for Cut-free Classical Analysis and Related Systems, Diss.Math., 118:50 pp.
Löb, M., 1955, Solution of a Problem of Leon Henkin, J.S.L., 20:115–118.
Mostowski, A., 1979, “Foundational Studies, I, II,” North Holland, Amsterdam.
Rogers, H., 1967, “Theory of Recursive Functions and Effective Computability,” McGraw-Hill, New York.
Shoenfield, J. R., 1967, “Mathematical Logic,” Addison-Wesley, Reading.
Smorynski, C., 1980, Calculating Self-referential Statements, Fund. Math., 109:189–210.
Stepanov, V. I., 1982, On an Application of the Hierarchy-formulas of the Peaono Arithmetic, in: “6th All-Union Conference on Mathematical Logic,” Tiflis (in Russian).
Stepanov, V. I., 1982, The Second Order Arithmetic and Consistency of a First Order Theory, Usp. Math. Nauk, 4:177–178 (in Russian).
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Stepanov, V.I. (1985). The Incompleteness Theorems and Related Results for Nonconstructive Theories. In: Dorn, G., Weingartner, P. (eds) Foundations of Logic and Linguistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0548-2_10
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DOI: https://doi.org/10.1007/978-1-4899-0548-2_10
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