论文标题
超越原子集：一阶逻辑的确定性
Beyond sets with atoms: definability in first order logic
论文作者
论文摘要
带有原子的集合可以替代ZFC基础数学基础，其中一些无限的（尽管高度对称的集合）以有限的方式行事。因此，人们可以尝试将经典算法从有限结构到某些无限结构进行分析。最近的结果表明，这确实是可能的，并导致许多实际应用。在本文中，我们将采取另一条途径来对无限集的有限分析，该套件扩展并提供了更多的原子套装。作为我们理论的应用，我们给出了可以在一阶逻辑片段中定义的自动机识别的语言的表征。
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite structures to some infinite structures. Recent results show that this is indeed possible and leads to many practical applications. In this paper we shall take another route to finite analysis of infinite sets, which extends and sheds more light on sets with atoms. As an application of our theory we give a characterisation of languages recognized by automata definable in fragments of first-order logic.
