Elementary Properties of Rogers Semilattices of Arithmetical Numberings
نویسنده
چکیده
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 computability theory , our main references are the textbooks of A.I. Mal'tsev [1], H. Rogers [2] and R. Soare [3]. For the main concepts and notions of the theory of numberings we refer to the book of Yu.L. Ershov [4].
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