和谐性质及其应用Ⅱ

Consistency Property and Its Application Ⅱ

Kim B.Bruce于1978年提出了三价逻辑L(Q)的逻辑公理系统。H.J.Keisler在1971年发表了无穷逻辑中的模型论一书,提出了无穷逻辑的公理系统,文中结合上述两种逻辑系统的思想,应用了无穷逻辑中的模型论一书中介绍的和谐性质的方法,建立了无穷逻辑中的二阶语言Lw1w(Q)的公理系统及模型理论。这部分主要是对Lw1w(Q)中的省略型定理及素模型定理的证明。

Kim B.Bruce gave a system of axioms for second order logic L(Q).H.J.Keisler in 1977 published a book called 《Model Theory for Infinitary Logic》 to give a system of axioms for infinitary logic. This article combines the two ideas of the two systems of axioms, applying the consistency property introduced by the book 《Model Theory for Infinitary Logic》 to give a system of axioms and model theory for infinitary second order logic Lw1w(Q). This part of the article is mainly the proofs of omitting type theorem for Lw1w (Q) and prime model theorem for Lw1w(Q).