On a problem of Cooper and Epstein
Journal of Symbolic Logic 68 (1):52-64 (2003)
| Abstract | In "Bounding minimal degrees by computably enumerable degrees" by A. Li and D. Yang, (this Journal, [1998]), the authors prove that there exist non-computable computably enumerable degrees c > a > 0 such that any minimal degree m being below c is also below a. We analyze the proof of their result and show that the proof contains a mistake. Instead we give a proof for the opposite result | |||||||||
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Rachel Epstein (2008). Prime Models of Computably Enumerable Degree. Journal of Symbolic Logic 73 (4):1373-1388.
William C. Calhoun & Manuel Lerman (2001). Embedding Finite Lattices Into the Ideals of Computably Enumerable Turing Degrees. Journal of Symbolic Logic 66 (4):1791-1802.
Rodney G. Downey, Geoffrey L. Laforte & Richard A. Shore (2003). Decomposition and Infima in the Computably Enumerable Degrees. Journal of Symbolic Logic 68 (2):551-579.
S. B. Cooper (1974). Minimal Pairs and High Recursively Enumerable Degrees. Journal of Symbolic Logic 39 (4):655-660.
S. Barry Cooper & Angsheng Li (2002). Splitting and Nonsplitting, II: A $Low_2$ C.E. Degree Above Which 0' is Not Splittable. Journal of Symbolic Logic 67 (4):1391-1430.
Peter Cholak, Rod Downey & Stephen Walk (2002). Maximal Contiguous Degrees. Journal of Symbolic Logic 67 (1):409-437.
William C. Calhoun (2006). Degrees of Monotone Complexity. Journal of Symbolic Logic 71 (4):1327 - 1341.
S. Barry Cooper, Angsheng Li, Andrea Sorbi & Yue Yang (2005). Bounding and Nonbounding Minimal Pairs in the Enumeration Degrees. Journal of Symbolic Logic 70 (3):741 - 766.
Theodore A. Slaman & John R. Steel (1989). Complementation in the Turing Degrees. Journal of Symbolic Logic 54 (1):160-176.
Angsheng Li & Dongping Yang (1998). Bounding Minimal Degrees by Computably Enumerable Degrees. Journal of Symbolic Logic 63 (4):1319-1347.
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