一、导言现代逻辑发展的主流,自从布尔(G.Boole)到弗雷格(G.Freqe)的开创性时期以来,沿着数学兴趣和应用的方向发展,取得了十分显著的进步。事实上,数学今天仍然占据着逻辑舞台的中心。这可以举出许多例证。例如,所谓逻辑的“算术部分”,包括算法理论、递归函数、λ转换演算,可计算性和一般能以过程的逻辑理论等作为最重要的部分突现. I. INTRODUCTION The mainstream of modern logic has made remarkable strides since the pioneering period of G. Boere to G. Freqe along the lines of interest and application in mathematics. In fact, mathematics still occupies the center of the logical stage today. Here are some examples. For example, so-called “arithmetic parts” of logic, including algorithmic theory, recursive functions, λ-conversion calculus, computability and, in general, process theory can be the most important part.