Limitwise monotonic functions, sets, and degrees on computable domains

Journal of Symbolic Logic 75 (1):131-154 (2010)
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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 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.

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Citations of this work

Torsion-Free Abelian Groups with Optimal Scott Families.Alexander G. Melnikov - 2018 - Journal of Mathematical Logic 18 (1):1850002.
The Kierstead's Conjecture and Limitwise Monotonic Functions.Guohua Wu & Maxim Zubkov - 2018 - Annals of Pure and Applied Logic 169 (6):467-486.

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References found in this work

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.
Computability Theory and Linear Orders.Rod Downey - 1998 - In I͡Uriĭ Leonidovich Ershov (ed.), Handbook of Recursive Mathematics. Elsevier. pp. 138--823.
Η-Representation of Sets and Degrees.Kenneth Harris - 2008 - Journal of Symbolic Logic 73 (4):1097-1121.
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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