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On the definition of a Lachlan semilattice

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    S. Yu. Podzorov

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  1. S. Yu. Podzorov
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Additional information

Original Russian Text Copyright © 2006 Podzorov S. Yu.

The author was partially supported by the Program “Universities of Russia” (Grant UR.04.01.013), KTsFE (Grant PD02-1.1-475), and the Russian Foundation for Basic Research (Grant 05-01-00819).

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Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Zhurnal, Vol. 47, No. 2, pp. 383–393, March–April, 2006.

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Podzorov, S.Y. On the definition of a Lachlan semilattice. Sib Math J 47, 315–323 (2006). https://doi.org/10.1007/s11202-006-0045-2

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  • DOI: https://doi.org/10.1007/s11202-006-0045-2

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