Decision times of infinite computations

11/10/2020 ∙ by Merlin Carl, et al. ∙ 0

The decision time of an infinite time algorithm is the supremum of its halting times over all real inputs. The decision time of a set of reals is the least decision time of an algorithm that decides the set; semidecision times of semidecidable sets are defined similary. It is not hard to see that ω_1 is the maximal decision time of sets of reals. Our main results determine the supremum of countable decision times as σ and that of countable semidecision times as τ, where σ and τ denote the suprema of Σ_1- and Σ_2-definable ordinals, respectively, over L_ω_1. We further compute analogous suprema for singletons.

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