Abstract
This chapter discusses applications of constructive mathematics for investigations of semantic questions and theories of intuitionistic choice sequences. Some general inductive definitions are introduced into constructive mathematics. For example, the suggested conception is applied to the study of Markov's semantics of constructive arithmetic and for building some models for intuitionistic theories. An example of the model for the theory of Kreisel's lawless sequences is described. The chapter considers constructive mathematics as a direction in mathematics. Various directions in mathematics differ from one another in two main respects: a) the objects of investigation, and b) the method of proving theorems about these objects. The primitive objects of investigation in constructive mathematics are elements of (intuitive) decidable classes of constructive objects. The primitive objects of investigations of intuitionistic mathematics are of different types. These are constructive objects, choice sequences, and species of intuitionistic objects. The most familiar objects of intuitionism are choice sequences that deal with natural numbers.
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