Algebra and Logic

, Volume 37, Issue 1, pp 21–34 | Cite as

Families with one-element Rogers semilattice

  • S. S. Goncharov
  • S. A. Badaev


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.


Recursive Function Numeration Theory Trivial Consequence Computable Enumeration Construction Step 
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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • S. S. Goncharov
  • S. A. Badaev

There are no affiliations available

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