一阶算术非标准模型的满意类
Satisfaction classes in nonstandard models of first-order arithmetic
摘要：
满足类是一组尊重塔斯基真值定义的非标准句子。我们主要对完全满意的课程感兴趣，即，满意度类决定了所有的非标准句。Kotlarski，Krajorski和Lachlan在1981年证明了PA的可数模型允许一个满意类当且仅当它是递归饱和的。本文详细地给出了这一事实的证明，它适用于具有函数符号的语言。满意度类只能在公式中看到深度的想法被扩展到术语。该定义引起了新的概念的估值的非标准条款，这些进行了调查。引入了自由满意类的概念，它是一个不需要非标准项存在性假设的满意类。众所周知，病态出现在某些满意度等级中。如何消除这些问题的想法将在最后一章中提出。这主要是通过将推理规则添加到M逻辑来实现的。许多这些扩展的一致性是一个悬而未决的问题。
英文摘要：
A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively saturated. A proof of this fact is presented in detail in such a way that it is adaptable to a language with function symbols. The idea that a satisfaction class can only see finitely deep in a formula is extended to terms. The definition gives rise to new notions of valuations of nonstandard terms; these are investigated. The notion of a free satisfaction class is introduced, it is a satisfaction class free of existential assumptions on nonstandard terms. It is well known that pathologies arise in some satisfaction classes. Ideas of how to remove those are presented in the last chapter. This is done mainly by adding inference rules to M-logic. The consistency of many of these extensions is left as an open question.
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。
