Geodesic
The universal Lachlan semilattice without the greatest element
Algebra i logika, Tome 46 (2007) no. 3, pp. 299-345.

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We deal with some upper semilattices of $m$-degrees and of numberings of finite families. It is proved that the semilattice of all c.e. $m$-degrees, from which the greatest element is removed, is isomorphic to the semilattice of simple $m$-degrees, the semilattice of hypersimple $m$-degrees, and the semilattice of $\Sigma_2^0$-computable numberings of a finite family of $\Sigma_2^0$-sets, which contains more than one element and does not contain elements that are comparable w.r.t. inclusion.
Keywords: upper semilattice, distributive semilattice, $m$-degree, numbering, Rogers semilattice, Lachlan semilattice. 
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S. Yu. Podzorov. The universal Lachlan semilattice without the greatest element. Algebra i logika, Tome 46 (2007) no. 3, pp. 299-345. http://geodesic.mathdoc.fr/item/AL_2007_46_3_a2/

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