This article is cited in 24 papers

Local Structure of Rogers Semilattices of $\Sigma^0_n$-Computable Numberings

S. Yu. Podzorov

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

Abstract: We deal in specific features of the algebraic structure of Rogers semilattices of $\Sigma^0_n$ – computable numberings, for $n\geqslant2$. It is proved that any Lachlan semilattice is embeddable (as an ideal) in such every semilattice, and that over an arbitrary non $0'$-principal element of such a lattice, any Lachlan semilattice is embeddable (as an interval) in it.

Keywords: Rogers semilattice, Lachlan semilattice, $\Sigma^0_n$-computable numbering.

UDC: 510.5

Received: 23.04.2004

 English version: Algebra and Logic, 2005, 44:1, 82–94

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