单子转导与拟阵的可定义类
Monadic transductions and definable classes of matroids
AI总结：
本文系统建立拟阵单子二阶转导理论，证明后向翻译定理，并据此证明格路拟阵类与尖刺子式类可由单子二阶逻辑定义。
摘要：
转导为我们提供了一种使用结构的单子二阶语言来陈述有关派生结构的方法。任何转导都会在这些结构的集合上诱导出一种关系。本文对拟阵单子二阶语言的转导理论进行了自洽阐述，其中包括证明拟阵版本的后向翻译定理，该定理将应用于转导像的任意公式提升为可应用于原像的公式。应用方面包括证明格路拟阵类和尖刺子式类均可由单子二阶逻辑中的语句定义。
英文摘要：
A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on the set of these structures. This article presents a self-contained presentation of the theory of transductions for the monadic second-order language of matroids. This includes a proof of the matroid version of the Backwards Translation Theorem, which lifts any formula applied to the images of the transduction into a formula which we can apply to the pre-images. Applications include proofs that the class of lattice-path matroids and the class of spike-minors can be defined by sentences in monadic second-order logic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
