Third-order functionals on partial combinatory algebras
نویسندگان
چکیده
Computability relative to a partial function f on the natural numbers can be formalized using notion of an oracle for this f. This generalized arbitrary combinatory algebras, yielding ‘adjoining algebra A’. A similar construction is known second-order functionals, but third-order case more difficult. In paper, we prove several results case. Given functional Φ A, show how construct A[Φ] where ‘computable’, and which has ‘lax’ factorization property (Theorem 7.3 below). Moreover, that, level first-order functions, effect making computable described as adding function.
منابع مشابه
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2023
ISSN: ['0168-0072', '1873-2461']
DOI: https://doi.org/10.1016/j.apal.2022.103205