带阶乘运算的一阶Peano算术系统中的Berry-like语句
The Berry-like Sentence in the First-order Peano Arithmetic System with the Operation of Factorial
摘要：
介绍了一种带阶乘运算的一阶Peano算术系统（PAF）。对于PAF中任意一个含有自由变元x的公式A（x），定义了一个相应的B-公式，即当A（x）可满足时，在满足公式A（x）的所有自然数中，存在唯一的最小数满足B-公式.然后，我们构造了一个公式，表示“存在x，对于任何一个哥德尔码小于小于常数a的B-公式，x不满足这个B-公式，并且x是具有这种特征的数中最小的。“然而，构造的公式本身是一个B-公式，它的哥德尔码小于a。因此，这是一个版本的PAF贝里句子“最小的正整数不能命名的11个字以下”，本身只有10个字。
英文摘要：
A first-order Peano Arithmetical system with the operation of factorial (PAF) is introduced. For any formula A(x) with a free variable x in PAF, we define a corresponding B-formula which means that there exists unique number that is smallest in all natural numbers satisfying the formula A(x) that satisfies the B-formula if A(x) is satisfiable. And then, we construct a formula which means that "there exists x, for any B-formula whose Godel code is smaller than a constant a, x does not satisfy this B-formula, and x is the smallest in those numbers that have such character." However, the constructed formula itself is a B-formula and its Godel code is smaller than a. Thus, it is a version in PAF of the Berry sentence "The smallest positive integer not nameable in under eleven words" that itself is in only ten words.
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。
