# Bounds on continuous Scott rank

@article{Chan2020BoundsOC, title={Bounds on continuous Scott rank}, author={William Chan and Ruiyuan Chen}, journal={Proceedings of the American Mathematical Society}, year={2020} }

An analog of Nadel's effective bound for the continuous Scott rank of metric structures, developed by Ben Yaacov, Doucha, Nies, and Tsankov, will be established: Let $\mathscr{L}$ be a language of continuous logic with code $\hat{\mathscr{L}}$. Let $\Omega$ be a weak modulus of uniform continuity with code $\hat{\Omega}$. Let $\mathcal{D}$ be a countable $\mathscr{L}$-pre-structure. Let $\bar{\mathcal{D}}$ denote the completion structure of $\mathcal{D}$. Then $\mathrm{SR}_\Omega(\bar{D}) \leq…

## 3 Citations

Polish G-spaces, the generalized model theory and complexity

- Mathematics
- 2019

Given Polish space ${\bf Y}$ and continuous language $L$ we study the corresponding logic $\mathsf{Iso}({\bf Y})$-space ${\bf Y}_L$. We build a framework of generalized model theory towards analysis…

AN INTRODUCTION TO THE SCOTT COMPLEXITY OF COUNTABLE STRUCTURES AND A SURVEY OF RECENT RESULTS

- PhilosophyThe Bulletin of Symbolic Logic
- 2021

Abstract Every countable structure has a sentence of the infinitary logic
$\mathcal {L}_{\omega _1 \omega }$
which characterizes that structure up to isomorphism among countable structures. Such a…

Bounds on Scott ranks of some polish metric spaces

- Mathematics, ArtJ. Math. Log.
- 2021

The Scott rank of [Formula: see text] is countable and in fact less than the Church–Kleene ordinal in the natural first-order language of metric spaces.

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Bounds on Scott ranks of some polish metric spaces

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The Scott rank of [Formula: see text] is countable and in fact less than the Church–Kleene ordinal in the natural first-order language of metric spaces.

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