Generalized computable numerations and nontrivial rogers semilattices

We outline the general approach to the notion of a computable numeration in the frames of which computable numerations, of families of arithmetic sets are studied. Supported by RECO grant NERBCHRXCT 930415 and by RFFR grant No. 096-01-01525 Supported by RECO grant NERBCIPDCT 940615 Translated fromAlgebra i Logika, Vol. 36, No. 6, pp. 621–641, November-December, 1997.