Remarks on Constructive Mathematical Analysis

Publisher Summary This chapter discusses the questions of constructive mathematics (CM), the fundamental principles of this trend in mathematics, and results concerning constructive mathematical analysis, obtained within the Prague seminar. The purpose of CM was to find foundations for mathematics that would be simple, secure, free from too far reaching idealizations, and foundations in which the concept of affectivity would be the principal. The chapter discusses the basic features of CM: (1) constructive objects are studied, (2) the abstraction of potential realizability and theory of algorithms are used, and (3) a specific interpretation of mathematical propositions is used. The main subject of CM is the study of the possibilities of the algorithmic transformation of coded information about mathematical objects. This fact delimitates the space in which CM can be developed, and it distinguishes CM from the intuitionistic program and other constructive trends.