  The minimum classical extension S$^{+g}$ of a constructive theory S based on
intuitionistic logic is defined by adding to S the G\"odel negative
interpretations of its classically correct mathematical axioms. First and
second order (primitive recursive) intuitionistic arithmetic are their own
minimum classical extensions, but intuitionistic recursive analysis cannot even
prove the negative interpretation of its quantifier-free countable choice
axiom. Variants of Kuroda's double negation shift schema (including the
G\"odel-Dyson-Kreisel axiom equivalent to the weak completeness of
intuitionistic predicate logic) and weak comprehension principles provide neat
characterizations of the minimum classical extensions of many classically
correct subsystems of Kleene's intuitionistic analysis I which are of interest
to constructive mathematicians. Some questions are left open.
