论文标题
算术中的不明智和满意度课程
Indiscernibles and satisfaction classes in arithmetic
论文作者
论文摘要
我们研究了PAI理论（Peano算术和不可分割的算术）。 PAI的模型是形式（M，i），其中M是PA的模型，I是M上不受限制的订单集合，（M，i）满足了公式的扩展感应方案。 定理A.让M成为任何基数的PA的非标准模型。 M对PAI iff M模型的扩展具有感应性部分满意度类别。 定理A产生以下推论，该推论提供了可计数的PA的可计数饱和模型的新表征： 推论。 IFF M的可数模型M被递归饱和，对PAI模型具有扩展。 定理B.通过将一单位谓词i（x）添加到算术语言中获得的语言中有一个句子，因此，鉴于任何基础性的任何非标准模型m，m对PAI + s iff m的模型具有扩展，具有感应性的完全满意度。
We investigate the theory PAI (Peano Arithmetic with Indiscernibles). Models of PAI are of the form (M, I), where M is a model of PA, I is an unbounded set of order indiscernibles over M, and (M, I) satisfies the extended induction scheme for formulae mentioning I. Our main results are Theorems A and B below. Theorem A. Let M be a nonstandard model of PA of any cardinality. M has an expansion to a model of PAI iff M has an inductive partial satisfaction class. Theorem A yields the following corollary, which provides a new characterization of countable recursively saturated models of PA: Corollary. A countable model M of PA is recursively saturated iff M has an expansion to a model of PAI. Theorem B. There is a sentence s in the language obtained by adding a unary predicate I(x) to the language of arithmetic such that given any nonstandard model M of PA of any cardinality, M has an expansion to a model of PAI + s iff M has a inductive full satisfaction class.
