Theories of Rogers Semilattices of Analytical Numberings
Bazhenov N.A. Mustafa M. Tleuliyeva Z.
April 2021Pleiades journals
Lobachevskii Journal of Mathematics
2021#42Issue 4701 - 708 pp.
Abstract: The paper studies Rogers semilattices, i.e. upper semilattices induced by the reducibility between numberings. Under the assumption of Projective Determinacy, we prove that for every non-zero natural number n, there are infinitely many pairwise elementarily non-equivalent Rogers semilattices for Σn1-computable families.
analytical hierarchy , elementary theory , projective determinacy , Rogers semilattice , theory of numberings , upper semilattice
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Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan
Sobolev Institute of Mathematics
Department of Mathematics
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