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AN INTRODUCTION TO THE SCOTT COMPLEXITY OF COUNTABLE STRUCTURES AND A SURVEY OF RECENT RESULTS
Published online by Cambridge University Press: 15 November 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 sentence is called a Scott sentence, and can be thought of as a description of the structure. The least complexity of a Scott sentence for a structure can be thought of as a measurement of the complexity of describing the structure. We begin with an introduction to the area, with short and simple proofs where possible, followed by a survey of recent advances.
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- © The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
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