English

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

Logic 2020-11-10 v1

Abstract

Every countable structure has a sentence of the infinitary logic Lω1ω\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.

Keywords

Cite

@article{arxiv.2011.03923,
  title  = {An introduction to the Scott complexity of countable structures and a survey of recent results},
  author = {Matthew Harrison-Trainor},
  journal= {arXiv preprint arXiv:2011.03923},
  year   = {2020}
}