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

笨拙處理

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.

憤慨點吧

串通

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

跳動

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

褪色

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.

上流社會

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.