Solovay reducibility and continuity | Zendy

Masahiro Kumabe | Zendy; Kenshi Miyabe | Zendy; Yuki Mizusawa | Zendy; Toshio Suzuki | Zendy

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Solovay reducibility and continuity

Author(s) -

Masahiro Kumabe,

Kenshi Miyabe,

Yuki Mizusawa,

Toshio Suzuki

Publication year - 2020

Publication title -

journal of logic and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.278

H-Index - 4

ISSN - 1759-9008

DOI - 10.4115/jla.2020.12.2

Subject(s) - reduction (mathematics) , mathematics , randomness , computable function , lipschitz continuity , discrete mathematics , combinatorics , pure mathematics , statistics , geometry

The objective of this study is a better understanding of the relationships between reducibility and continuity. Solovay reducibility is a variation of Turing reducibility based on the distance of two real numbers. We characterize Solovay reducibility by the existence of a certain real function that is computable (in the sense of computable analysis) and Lipschitz continuous. We ask whether there exists a reducibility concept that corresponds to Hölder continuity. The answer is affirmative. We introduce quasi Solovay reducibility and characterize this new reducibility via Hölder continuity. In addition, we separate it from Solovay reducibility and Turing reducibility and investigate the relationships between complete sets and partial randomness. 2010 Mathematics Subject Classification 03D78 (primary); 68Q30 (secondary)

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