Computable reducibility of equivalence relations and an effective jump operator

John D. Clemens; Samuel Coskey; Gianni Krakoff

doi:10.1017/jsl.2022.45

Computable reducibility of equivalence relations and an effective jump operator

John D. Clemens, Samuel Coskey, Gianni Krakoff

Mathematics Department

Boise State University

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

1 Scopus citations

Abstract

We introduce the computable FS-jump, an analog of the classical Friedman-Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).

Original language	English
Pages (from-to)	540-561
Number of pages	22
Journal	Journal of Symbolic Logic
Volume	88
Issue number	2
DOIs	https://doi.org/10.1017/jsl.2022.45
State	Published - 13 Jun 2023

Keywords

ceers
computable reducibility
hyperarithmetic equivalence relations.

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10.1017/jsl.2022.45

Cite this

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abstract = "We introduce the computable FS-jump, an analog of the classical Friedman-Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).",

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AU - Coskey, Samuel

AU - Krakoff, Gianni

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PY - 2023/6/13

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N2 - We introduce the computable FS-jump, an analog of the classical Friedman-Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).

AB - We introduce the computable FS-jump, an analog of the classical Friedman-Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).

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KW - computable reducibility

KW - hyperarithmetic equivalence relations.

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M3 - Article

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Computable reducibility of equivalence relations and an effective jump operator

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