Abstract
We study existence problems of maximal antichains in the Turing degrees. In particular, we give a characterization of the existence of thin \(\Pi^1_1\) maximal antichains in the Turing degrees in terms of (relatively) constructible reals. A corollary of our main result gives a negative solution to a question of Jockusch under the assumption that every real is constructible.
The research of the authors was respectively supported in part by NUS grant WBS 146-000-054-123, and NSF of China No. 10471060 and No. 10420130638.
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Chong, C.T., Yu, L. (2007). Thin Maximal Antichains in the Turing Degrees. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_17
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DOI: https://doi.org/10.1007/978-3-540-73001-9_17
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