This article is cited in 2 papers

On the definition of a Lachlan semilattice

S. Yu. Podzorov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We study the algorithmic properties of the semilattices introduced in 1972 by Lachlan in his work on recursively enumerable $m$-degrees, the so-called Lachlan semilattices. We show that in Lachlan's definition the effectivity condition on the meet can be omitted in the sequence determining such a semilattice.

Keywords: distributive semilattice, $m$-degree, arithmetic hierarchy, computable enumeration.

UDC: 510.5

Received: 26.04.2004

 English version: Siberian Mathematical Journal, 2006, 47:2, 315–323

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