The universal Lachlan semilattice without the greatest element |
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Authors: | S Yu Podzorov |
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Institution: | (1) Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia |
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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 Σ
2
0
-computable numberings of a finite family of Σ
2
0
-sets, which contains more than one element and does not contain elements that are comparable w.r.t. inclusion.
Supported by the Grant Council (under RF President) for Young Russian Scientists via project MK-1820.2005.1.
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Translated from Algebra i Logika, Vol. 46, No. 3, pp. 299–345, May–June, 2007. |
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Keywords: | upper semilattice distributive semilattice m-degree numbering Rogers semilattice Lachlan semilattice |
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