向前向后法证明一阶逻辑的几个定理

Proving Several Theorems in First Order Logic Based on Back-and-Forth Method

向前向后方法是模型论及其应用研究中的一个很重要的工具 .一阶逻辑的内插定理和保持定理确定了符合某些条件的公式的存在性 ,经典模型论中对这些的证明较为繁难 .文中使用向前向后方法 ,对有限语言下一阶逻辑的内插定理和保持定理等几个定理 ,给出一种简洁的证明 .

Back-and-forth method is an important tool for studying model theory and its application. Interpolation theorem and preservation theorem in first order logic have determined the existence of first order formula in accordance with certain conditions, their proofs in classical model theory are fairly long and hard to tackle. By using back-and-forth method, the author gives interpolation theorem and preservation theorems a kind of succinct proofs in finite language.