Journal of Symbolic Logic

Limitwise monotonic functions, sets, and degrees on computable domains

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.

Article information

Source
J. Symbolic Logic Volume 75, Issue 1 (2010), 131-154.

Dates
First available in Project Euclid: 25 January 2010

http://projecteuclid.org/euclid.jsl/1264433912

Digital Object Identifier
doi:10.2178/jsl/1264433912

Zentralblatt MATH identifier
05681295

Mathematical Reviews number (MathSciNet)
MR2605885

Citation

Kach, Asher M.; Turetsky, Daniel. Limitwise monotonic functions, sets, and degrees on computable domains. Journal of Symbolic Logic 75 (2010), no. 1, 131--154. doi:10.2178/jsl/1264433912. http://projecteuclid.org/euclid.jsl/1264433912.