Abstract
Oracle Turing machines and Turing reductions are defined and discussed.
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- 1.
In Chap. 2, we used the power set operation to obtain an infinite sequence of ever larger sets. By Lemma 2.2, all pairs of sets are comparable in cardinality. The question of whether there exists a set strictly larger than the integers but smaller than the reals is the famous “continuum hypothesis;” it’s a long story (see [Coh]).
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Supowit, K.J. (2023). Reductions, Comparability (Kleene-Post 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_5
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DOI: https://doi.org/10.1007/978-3-031-26904-2_5
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