Limitwise Monotonic Functions and Their Applications
نویسندگان
چکیده
We survey what is known about limitwise monotonic functions and sets and discuss their applications in effective algebra and computable model theory. Additionally, we characterize the computably enumerable degrees that are totally limitwise monotonic, show the support strictly increasing 0′-limitwise monotonic sets on Q do not capture the sets with computable strong η-representations, and study the limitwise monotonic spectra of a set.
منابع مشابه
Limitwise monotonic sets of reals
1. f (x, s) f (x, s + 1) for all x and s; 2. sups f (x, s) < ∞ for every x ; 3. F(x) = sups f (x, s). A set A ⊆ N is limitwise monotonic if A equals to the range of some limitwise monotonic function. If we replace here the computable functions f by X -computable functions for some Turing oracle X then we get the notions of X -limitwise monotonic functions and sets, respectively. Note that a sim...
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تاریخ انتشار 2009