和谐性质及其应用Ⅰ

Consistency Property and Its Application I

Bruce于1978年提出二阶逻辑L(Q)的概念和公理系统。Keisler提出了无穷逻辑的公理系统。本文结合上述两种逻辑系统的思想,应用和谐性质的方法,建立了无穷逻辑中的二阶语言Lw_1w(Q)的公理系统及模型理论。此文证明了主要是对Lw_1w(Q)中的模型存在定理及推演完全性定理。

Kim B. Bruce gave a system of axioms lor second order logic L(Q). H. J. Keisler presented a system of axioms for infinilary logic. This article gives a system of axioms and model theory for infinitary second order logic ZWIW(Q), based on the combination of both ideas of the systems and application of the consistency property; proves the model existence theorem and completeness theorem in Lw1w(Q).