Families with one-element Rogers semilattice
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We are concerned with Ershov’s problem of obtaining a characterization of families with one-element Rogers semilattice (the semilattice of computable enumerations of a family). An algorithmic description is furnished for the families of recursive functions whose Rogers semilattice is one-element. It is proved that there exists a nontrivial family of recursively enumerable sets with the least set under inclusion, whose Rogers semilattice consists of a single element.
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