Geodesic
A semilattice generated by superlow computably enumerable degrees
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2011), pp. 85-90.

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We prove that a partially ordered set of all computably enumerable (c.e.) degrees that are the least upper bounds of two superlow c.e. degrees is an upper semilattice not elementary equivalent to the semilattice of all c.e. degrees.
Mots-clés : superlow degrees, low degrees, totally c.e. degrees, critical triples. 
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M. Kh. Faizrakhmanov. A semilattice generated by superlow computably enumerable degrees. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2011), pp. 85-90. https://geodesic-test.mathdoc.fr/item/IVM_2011_1_a7/

[1] Carstens H. G., “$\Delta^0_2$-Mengen”, Arch. Math. Logik Grundlagenforsch., 18 (1976), 55–65 | DOI | MR | Zbl

[2] Cholak P., Downey R., Greenberg N., “Strong jump-traceability. I. The computably enumerable case”, Adv. Math., 217:5 (2008), 2045–2074 | DOI | MR | Zbl

[3] Nies A., “Lowness properties and randomness”, Adv. Math., 197:1 (2005), 274–305 | DOI | MR | Zbl

[4] Nies A., “Reals which compute little”, Logic Colloquium' 02, Lect. Notes Log., 27, Assoc. Symbol. Logic, La Jolla, CA, 2006, 261–275 | MR | Zbl

[5] Downey R. G., Greenberg N., Weber R., “Totally $\omega$-computably enumerable degrees and bounding critical triples”, J. Math. Logic, 7:2 (2007), 145–171 | DOI | MR | Zbl

[6] Walk S., Towards a definition of the array computable degrees, Ph. D. Thesis, University of Notre Dame, 1999

[7] Sacks G. E., “On the degrees less than $\mathbf{0}'$”, Ann. Math., 2:77 (1963), 211–231 | DOI | MR | Zbl

[8] Bickford M., Mills F., Lowness properties of r. e. sets, Manuscript, University of Wisconsin-Madison, 1982

[9] Schaeffer B., “Dynamic notions of genericity and array noncomputability”, Ann. Pure Appl. Logic, 95:1–3 (1998), 37–69 | DOI | MR | Zbl

[10] Soar R. I., Vychislimo perechislimye mnozhestva i stepeni, Kazanskoe matematicheskoe o-vo, Kazan, 2000 | MR | Zbl