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… 
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3 Citations

3 Citations

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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
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
TLDR
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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