Abstract
In Chaps. 11 and 12, the branches emanating from a tree node correspond to guesses about the given set A. In this chapter and in Chap. 14, they correspond to guesses about the construction. Also, presented here are a few other innovations, including the “joint custody” technique.
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Notes
- 1.
This is an algorithms book. It is primarily about algorithms for constructing c.e. sets to meet various collections of requirements. Hence, the reader may skip the proof of this lemma without loss of continuity.
- 2.
It might be that neither the A-side nor the B-side is injured during stage \(t_i\). In that case, both sides would maintain custody of the value \(\Phi _e^A(p)[t_i]\) from the start of stage \(t_i\) to the start of stage \(t_{i+1}\).
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Supowit, K.J. (2023). Joint Custody (Minimal Pair 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_13
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DOI: https://doi.org/10.1007/978-3-031-26904-2_13
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