Titlebook: Algorithms for Constructing Computably Enumerable Sets; Kenneth J. Supowit Textbook 2023 The Editor(s) (if applicable) and The Author(s),

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Set Theory, Requirements, Witnesses,This is a very brief introduction to infinite cardinals. Our main interest here is in “requirements” and in “witnesses,” which are key concepts throughout this book.

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串通

Priorities (A Splitting Theorem),A simple priority argument is motivated and presented.

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Reductions, Comparability (Kleene-Post Theorem),Oracle Turing machines and Turing reductions are defined and discussed.

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MODE

ANN

UTTER

,Length of Agreement (Sacks Splitting Theorem),Suppose that we are given a c.e.n. set ., and we wish to construct a c.e.n. set . having certain properties, including .. The length of agreement method, introduced here, is a way to do this.

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Limpid

,A Tree of Guesses (Weak Thickness Lemma),The priority tree, which we call a “tree of guesses,” is introduced, and used for a construction involving infinite injury. The associated concept of “.-believability” is employed.