Theories of Rogers Semilattices of Analytical Numberings

Nikolay Bazhenov; Manat Mustafa; Zhansaya Tleuliyeva

doi:10.1134/S1995080221040065

Theories of Rogers Semilattices of Analytical Numberings

Nikolay Bazhenov, Manat Mustafa, Zhansaya Tleuliyeva

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 Σ1n-computable families.

Original language	English
Article number	708
Pages (from-to)	701
Number of pages	8
Journal	Lobachevskii Journal of Mathematics
DOIs	https://doi.org/10.1134/S1995080221040065
Publication status	Accepted/In press - 2021

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title = "Theories of Rogers Semilattices of Analytical Numberings",

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 Σ1n-computable families.",

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AB - 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 Σ1n-computable families.

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DO - 10.1134/S1995080221040065

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JO - Lobachevskii Journal of Mathematics

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