Geodesic
Local Structure of Rogers Semilattices of $\Sigma^0_n$-Computable Numberings
Algebra i logika, Tome 44 (2005) no. 2, pp. 148-172

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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. 
@article{AL_2005_44_2_a1,
     author = {S. Yu. Podzorov},
     title = {Local {Structure} of {Rogers} {Semilattices} of~$\Sigma^0_n${-Computable} {Numberings}},
     journal = {Algebra i logika},
     pages = {148--172},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2005_44_2_a1/}
}
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S. Yu. Podzorov. Local Structure of Rogers Semilattices of $\Sigma^0_n$-Computable Numberings. Algebra i logika, Tome 44 (2005) no. 2, pp. 148-172. http://geodesic.mathdoc.fr/item/AL_2005_44_2_a1/