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A superhigh diamond in the c.e. tt-degrees. (English) Zbl 1216.03054
A computably enumerable set \(A\) is superhigh if \(A'\equiv_{\text{tt}}0''\) . In this paper it is proved that there are superhigh computably enumerable sets \(A\) and \(B\) such that \({\mathbf 0}\), \(\text{deg}_{\text{tt}}(A)\), \(\text{deg}_{\text{tt}}(B)\), and \({\mathbf 0}'_{\text{tt}}\) form a diamond in the computably enumerable tt-degrees.

MSC:
03D25 Recursively (computably) enumerable sets and degrees
03D30 Other degrees and reducibilities in computability and recursion theory
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[1] Cooper S.B.: Degrees of unsolvability complementary between recursively enumerable degrees I. Ann. Math. Logic 4, 31–73 (1972) · Zbl 0248.02045 · doi:10.1016/0003-4843(72)90011-3
[2] Downey R.: D.r.e. degrees and the nondiamond theorem. Bull. Lond. Math. Soc. 21, 43–50 (1989) · Zbl 0628.03030 · doi:10.1112/blms/21.1.43
[3] Epstein, R.L.: Minimal degrees of unsolvability and the full approximation construction. Mem. Amer. Math. Soc., 162(3), (1975) · Zbl 0315.02043
[4] Jockusch C.G. Jr, Mohrherr J.: Embedding the diamond lattice in the recursively enumerable truth-table degrees. Proc. Amer. Math. Soc. 94, 123–128 (1985) · Zbl 0534.03019
[5] Lachlan A.H.: Lower bounds for pairs of recursively enumerable degrees. Proc. Lond. Math. Soc. 16, 537–569 (1966) · Zbl 0156.00907 · doi:10.1112/plms/s3-16.1.537
[6] Martin D.: Classes of recursively enumerable sets and degrees of unsolvability. Z. Math. Logik Grundlag. Math. 12, 295–310 (1966) · Zbl 0181.30504 · doi:10.1002/malq.19660120125
[7] Mohrherr J.: A refinement of low n and high n for the r.e. degrees. Z. Math. Logik Grundlag. Math. 32, 5–12 (1986) · Zbl 0625.03022 · doi:10.1002/malq.19860320103
[8] Ng K.M.: On very high degrees. J. Symb. Logic 73, 309–342 (2008) · Zbl 1168.03031 · doi:10.2178/jsl/1208358755
[9] Simpson S.G.: Almost everywhere domination and superhighness. Math. Log. Q. 53, 462–482 (2007) · Zbl 1123.03040 · doi:10.1002/malq.200710012
[10] Soare R.I.: Recursively Enumerable Sets and Degrees. Springer, Heidelberg (1987) · Zbl 0667.03030
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