Journal of Mathematical Logic 21 (1):2150001 (2020)

Authors
William Chan
University of Manchester
Abstract
If [Formula: see text] is a proper Polish metric space and [Formula: see text] is any countable dense submetric space of [Formula: see text], then the Scott rank of [Formula: see text] in the natural first-order language of metric spaces is countable and in fact at most [Formula: see text], where [Formula: see text] is the Church–Kleene ordinal of [Formula: see text] which is the least ordinal with no presentation on [Formula: see text] computable from [Formula: see text]. If [Formula: see text] is a rigid Polish metric space and [Formula: see text] is any countable dense submetric space, then the Scott rank of [Formula: see text] is countable and in fact less than [Formula: see text].
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DOI 10.1142/s021906132150001x
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References found in this work BETA

Scott Rank of Polish Metric Spaces.Michal Doucha - 2014 - Annals of Pure and Applied Logic 165 (12):1919-1929.
Scott Sentences and Admissible Sets.Mark Nadel - 1974 - Annals of Mathematical Logic 7 (2):267.

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