Abstract
In this paper, we present proofs of properties of semirecursive sets based directly on the definition of these sets and on the recursiveness of Kleene predicates. These proofs are shorter and clearer than traditional proofs of similar statements for recursively enumerable sets.
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References
N. Cutland, Computability. An Introduction to Recursive Function Theory, Cambridge Univ., Cambridge (1980).
S. C. Kleene, Introduction to Metamathematics, P. Noordhoff, Groningen (1959).
A. I. Malcev, Algorithms and Recursive Functions [in Russian], Nauka, Moscow (1986).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 179, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, 2020.
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Timofeeva, I.L. On Proofs of Properties of Semirecursive Sets. J Math Sci 276, 423–427 (2023). https://doi.org/10.1007/s10958-023-06759-6
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DOI: https://doi.org/10.1007/s10958-023-06759-6
Keywords and phrases
- semirecursive set
- semicharacteristic function
- recursively enumerable set
- partially recursive function
- recursive function
- Kleene predicate