This article is cited in 4 papers

The universal Lachlan semilattice without the greatest element

S. Yu. Podzorov


Abstract: 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.

UDC: 510.5

Received: 24.06.2006
Revised: 21.02.2007

 English version: Algebra and Logic, 2007, 46:3, 163–187

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