  Although the axiom of choice is incompatible with both constructive and intuitionistic ZF, other choice principles may be added to the basic systems without producing the same undesirable results. For example one could add the principle of countable choice (AC\(_0)\) or that of dependent choice (DC). In fact,  both have been often employed in the constructive mathematical practice.  (For their exact formulation see the supplementary document on  Axioms of CZF and IZF.)