鹤滩上的裂缝：次度谓词
A Crevice on the Crane Beach: Finite-Degree Predicates
摘要：
本文证明了词上的一阶逻辑（FO）与配备有限数量谓词集的FO是等表达的，即顺序、二元谓词MSB $_0$和有限度谓词：FO[Arb] = FO[<，MSB $_0$，Fin]. Crane Beach Property（CBP）是在十多年前提出的，如果所有允许使用中性字母的可表达语言都是正则的，那么CBP就是一个逻辑。虽然已知FO[Arb]不具有CBP，但是这里示出了CBP的（强形式）对于FO[<，Fin]和FO[<，MSB $_0$ ]都成立。因此，FO[<，Fin]表现出局部性和CBP的形式，并且仍然可以表达各种各样的语言，而与FO[Arb]的表达能力相差一个简单的谓词。作为应用，研究了FO[<，Fin]的计数能力.
英文摘要：
First-order logic (FO) over words is shown to be equiexpressive with FO equipped with a restricted set of numerical predicates, namely the order, a binary predicate MSB$_0$, and the finite-degree predicates: FO[Arb] = FO[<, MSB$_0$, Fin]. The Crane Beach Property (CBP), introduced more than a decade ago, is true of a logic if all the expressible languages admitting a neutral letter are regular. Although it is known that FO[Arb] does not have the CBP, it is shown here that the (strong form of the) CBP holds for both FO[<, Fin] and FO[<, MSB$_0$]. Thus FO[<, Fin] exhibits a form of locality and the CBP, and can still express a wide variety of languages, while being one simple predicate away from the expressive power of FO[Arb]. The counting ability of FO[<, Fin] is studied as an application.
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。
