An introduction to the Scott complexity of countable structures and a survey of recent results

Matthew Harrison-Trainor

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arXiv · 2011.03923

An introduction to the Scott complexity of countable structures and a survey of recent results

Matthew Harrison-Trainor

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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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BibTeX RIS

Matthew Harrison-Trainor. 2020-11-08. An introduction to the Scott complexity of countable structures and a survey of recent results. https://arxiv.org/abs/2011.03923

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