Abstract
For any enumeration degree a let \(D^s_{\bf a}\) be the set of s-degrees contained in a. We answer an open question of Watson by showing that if a is a nontrivial \(\Sigma^0_2\)-enumeration degree, then \(D^s_{\bf a}\) has no least element. We also show that every countable partial order embeds into \(D^s_{\bf a}\).
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Kent, T.F. (2008). s-Degrees within e-Degrees. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2008. Lecture Notes in Computer Science, vol 4978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79228-4_50
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DOI: https://doi.org/10.1007/978-3-540-79228-4_50
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