论文标题
可计数结构的Scott复杂性的简介以及最近的结果调查
An introduction to the Scott complexity of countable structures and a survey of recent results
论文作者
论文摘要
每个可计数结构都有一个无限逻辑$ \ MATHCAL {l} _ {ω_1Ω} $的句子，它表征了可数结构中的同构的结构。这样的句子称为Scott句子，可以将其视为对结构的描述。斯科特句子的结构最小复杂性可以被认为是描述结构的复杂性的测量。我们首先介绍该地区，并在可能的情况下进行简短而简单的证据，然后对最近的进步进行调查。
Every countable structure has a sentence of the infinitary logic $\mathcal{L}_{ω_1 ω}$ 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.
