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arXiv · 1906.00351

The Scott rank of Polish metric spaces

Sy Friedman·Katia Fokina·Martin Koerwien·Andre Nies
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Abstract

We study the usual notion of Scott rank but in the setting of Polish metric spaces. The signature consists of distance relations: for each rational $q > 0$, there is a relation $R_{<q}(x,y)$ stating that the distance of $x$ and $y $ is less than $q$. We show that compact spaces have Scott rank at most $\omega$, and that there are discrete ultrametric spaces of arbitrarily high countable Scott rank.

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Sy Friedman, Katia Fokina, Martin Koerwien, Andre Nies. 2019-06-02. The Scott rank of Polish metric spaces. https://arxiv.org/abs/1906.00351

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