Limitwise monotonic functions, sets, and degrees on computable domains

Journal of Symbolic Logic 75 (1):131-154 (2010)
We extend the notion of limitwise monotonic functions to include arbitrary computable domains. We then study which sets and degrees are support 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 limitwise monotonic sets on certain domains.
Keywords Limitwise monotonic function   η-representation
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DOI 10.2178/jsl/1264433912
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Computable Models of Theories with Few Models.Bakhadyr Khoussainov, Andre Nies & Richard A. Shore - 1997 - Notre Dame Journal of Formal Logic 38 (2):165-178.
Computable Shuffle Sums of Ordinals.Asher M. Kach - 2008 - Archive for Mathematical Logic 47 (3):211-219.
Order-Computable Sets.Denis Hirschfeldt, Russell Miller & Sergei Podzorov - 2007 - Notre Dame Journal of Formal Logic 48 (3):317-347.

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