Limitwise monotonic functions, sets, and degrees on computable domains
Asher M. Kach, Daniel D. Turetsky · Journal of Symbolic Logic · 2010
Abstract We extend the notion of limitwise monotonic functions to include arbitrary computable domains. We then study which sets and degrees aresupport increasing (support strictly increasing)limitwise monotonic on various computable domains. As applications, we provide a characterization of the setsSwith computableincreasing η-representationsusing support increasing limitwise monotonic sets on ℚ and note relationships between the class oforder-computablesets and the class of support increasing (support strictly increasing) limitwise monotonic sets on certain domains.