Abstract
Suppose that we are given a c.e.n. set C, and we wish to construct a c.e. set A having certain properties, including \(A \le _T C\). Permitting, introduced here, is a way to do this.
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Notes
- 1.
When introducing the Friedberg-Muchnik algorithm in Chap. 7, we used the phrase “potential witness” to denote a number that may turn out to be a valid witness in this sense. We were tempted to distinguish between a “potential witness” and a “witness” (i.e., a potential witness that satisfies the full requirement, such as in (8.3)) throughout the remainder of this book. However, the phrase “potential witness” is too cumbersome, so instead we will distinguish between “witness” and “valid witness”.
- 2.
If you’re a computer programmer, think of j and x as “hard-coded” constants (also known as “magic numbers”), whereas p is an input passed to Algorithm 8.2.
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Supowit, K.J. (2023). Permitting (Friedberg-Muchnik Below C Theorem). In: Algorithms for Constructing Computably Enumerable Sets. Computer Science Foundations and Applied Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-26904-2_8
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DOI: https://doi.org/10.1007/978-3-031-26904-2_8
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