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 \(\Sigma^{1}_{n}\)-computable families.
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Funding
The work was supported by Nazarbayev University Faculty Development Competitive Research Grants 021220FD3851. The work of N. Bazhenov was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0002). M. Mustafa was also partially supported by MESRK grant no. AP08856834. Part of the research contained in this paper was carried out while N. Bazhenov was visiting the Department of Mathematics of Nazarbayev University, Nur-Sultan. The authors wish to thank Nazarbayev University for its hospitality.
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(Submitted by I. Sh. Kalimullin)
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Bazhenov, N.A., Mustafa, M. & Tleuliyeva, Z. Theories of Rogers Semilattices of Analytical Numberings. Lobachevskii J Math 42, 701–708 (2021). https://doi.org/10.1134/S1995080221040065
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DOI: https://doi.org/10.1134/S1995080221040065