7 found
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  1.  40
    Dominical Categories: Recursion Theory Without Elements.Robert A. di Paola & Alex Heller - 1987 - Journal of Symbolic Logic 52 (3):594-635.
    Dominical categories are categories in which the notions of partial morphisms and their domains become explicit, with the latter being endomorphisms rather than subobjects of their sources. These categories form the basis for a novel abstract formulation of recursion theory, to which the present paper is devoted. The abstractness has of course its usual concomitant advantage of generality: it is interesting to see that many of the fundamental results of recursion theory remain valid in contexts far removed from their classic (...)
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  2. Some Properties of the Syntactic P-Recursion Categories Generated by Consistent, Recursively Enumerable Extensions of Peano Arithmetic.Robert A. di Paola & Franco Montagna - 1991 - Journal of Symbolic Logic 56 (2):643-660.
  3.  22
    A Theorem on Shortening the Length of Proof in Formal Systems of Arithmetic.Robert A. di Paola - 1975 - Journal of Symbolic Logic 40 (3):398-400.
  4.  25
    A Lift of a Theorem of Friedberg: A Banach-Mazur Functional That Coincides with No Α-Recursive Functional on the Class of Α-Recursive Functions.Robert A. di Paola - 1981 - Journal of Symbolic Logic 46 (2):216-232.
    R. M. Friedberg demonstrated the existence of a recursive functional that agrees with no Banach-Mazur functional on the class of recursive functions. In this paper Friedberg's result is generalized to both α-recursive functionals and weak α-recursive functionals for all admissible ordinals α such that $\lambda , where α * is the Σ 1 -projectum of α and λ is the Σ 2 -cofinality of α. The theorem is also established for the metarecursive case, α = ω 1 , where α (...)
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  5.  11
    A Theorem on Shortening the Length of Proof in Formal Systems of Arithmetic.Robert A. di Paola - 1975 - Journal of Symbolic Logic 40 (3):398-400.
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  6. Pseudo-Complements and Ordinal Logics Based on Consistency Statements.Robert A. Di Paola - 1966 - Journal of Symbolic Logic 31 (3):359-364.
  7.  19
    Some Theorems on Extensions of Arithmetic.Robert A. Di Paola - 1967 - Journal of Symbolic Logic 32 (2):180-189.