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Title: Members of thin π⁰₁ classes and generic degrees
Authors: Stephan, Frank
Wu, Guohua
Yuan, Bowen
Keywords: Science::Mathematics
Issue Date: 2022
Source: Stephan, F., Wu, G. & Yuan, B. (2022). Members of thin π⁰₁ classes and generic degrees. Proceedings of the American Mathematical Society, 150(7), 3125-3131.
Project: MOE2016-T2-1-019 / R146-000-234-112
MOE2019-T2-2-121 / R146-000-304-112
MOE2016-T2-1-083 (M4020333)
RG32/16 (M4011672)
RG111/19 (M4012245)
Journal: Proceedings of the American Mathematical Society
Abstract: A π⁰₁ class P is thin if every π⁰₁ subclass Q of P is the intersection of P with some clopen set. In 1993, Cenzer, Downey, Jockusch and Shore initiated the study of Turing degrees of members of thin π⁰₁ classes, and proved that degrees containing no members of thin π⁰₁ classes can be recursively enumerable, and can be minimal degree below 0'. In this paper, we work on this topic in terms of genericity, and prove that all 2-generic degrees contain no members of thin π⁰₁ classes. In contrast to this, we show that all 1-generic degrees below 0' contain members of thin π⁰₁ classes.
ISSN: 0002-9939
DOI: 10.1090/proc/15325
Rights: © 2022 American Mathematical Society. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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