Page "Constructivism (mathematics)" Paragraph 21

The status of the axiom of choice in constructive mathematics is complicated by the different approaches of different constructivist programs.

One trivial meaning of " constructive ", used informally by mathematicians, is " provable in ZF set theory without the axiom of choice.

" However, proponents of more limited forms of constructive mathematics would not assert that ZF itself is a constructive system.