Constructivist mathematics [1] is an approach to math that restricts the universe of discourse to objects that can be explicitly defined. With this restriction,

Constructivist mathematics [1] is an approach to math that restricts the universe of discourse to objects that can be explicitly defined. With this restriction, the subset of the real numbers considered consists of the reals that are definable [2], such as those that are computable [3] and constructible [4]. Similarly, the axiom of choice allows for the existence of nondefinable choice functions [5] in certain cases, so is rejected. Regarding the part about analysis, the field of computable analysis [6] exists to establish analysis on constructivist footing. [1] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics) https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_... [2] https://en.wikipedia.org/wiki/Definable_real_number https://en.wikipedia.org/wiki/Definable_real_number [3] https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number [4] https://en.wikipedia.org/wiki/Constructible_number https://en.wikipedia.org/wiki/Constructible_number [5] https://en.wikipedia.org/wiki/Choice_function https://en.wikipedia.org/wiki/Choice_function [6] https://en.wikipedia.org/wiki/Computable_analysis https://en.wikipedia.org/wiki/Computable_analysis