ELEMENTARY PROPERTIES OF ROGERS SEMILATTICES OF ARITHMETICAL NUMBERINGS
S. A. Badaev, С. С. Гончаров, Andrea Sorbi · 2003
We investigate differences in the elementary theories of Rogers semilattices of arithmetical 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. 1. Preliminaries and Background 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].