### Limitwise monotonic functions, sets, and degrees on computable domains

Asher M. Kach and Daniel Turetsky
Source: J. Symbolic Logic Volume 75, Issue 1 (2010), 131-154.

#### Abstract

We extend the notion of limitwise monotonic functions to include arbitrary computable domains. We then study which sets and degrees are support increasing (support strictly increasing) limitwise monotonic on various computable domains. As applications, we provide a characterization of the sets S with computable increasing η-representations using support increasing limitwise monotonic sets on ℚ and note relationships between the class of order-computable sets and the class of support increasing (support strictly increasing) limitwise monotonic sets on certain domains.

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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1264433912
Digital Object Identifier: doi:10.2178/jsl/1264433912
Zentralblatt MATH identifier: 05681295
Mathematical Reviews number (MathSciNet): MR2605885

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