On Elementary Theories of Rogers Semilattices
نویسندگان
چکیده
Describing the elementary theories of Rogers semilattices is one of the main problems of the theory of numberings. For the classical case of computable families of computably enumerable sets, V.V. V’jugin showed in [1] the existence of infinitely many families with pairwise elementarily different Rogers semilattices. Nevertheless, the study of Rogers semilattices undertaken in recent years (see [2]–[5]) for families of sets at levels greater than one in the Kleene-Mostowsky hierarchy has shown
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Elementary Properties of Rogers Semilattices of Arithmetical Numberings
We investigate differences in the elementary theories of Rogers semilattices of arith-metical numberings, depending on structural invariants of the given families of arithmetical sets. It is shown that at any fixed level of the arithmetical hierarchy there exist infinitely many families with pairwise elementary different Rogers semilattices. For unexplained terminology and notations relative to...
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