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Limitwise monotonic functions, sets, and degrees on computable domains

Published online by Cambridge University Press:  12 March 2014

Asher M. Kach  and
Daniel Turetsky
Asher M. Kach
Affiliation:
University of Connecticut, Department of Mathematics, Storrs, CT 06269, USA, E-mail: kach@math.uconn.edu
Daniel Turetsky
Affiliation:
University of Wisconsin, Department of Mathematics, Madison, WI 53706, USA, E-mail: turetsky@math.wisc.edu
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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.

Keywords

Limitwise monotonic functionη-representation
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 1 , March 2010 , pp. 131 - 154
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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