  The purpose of this contribution is to give a coherent account of a
particular narrative which links locales, geometric theories, sheaf semantics
and constructive commutative algebra. We are hoping to convey a firm grasp of
three ideas: (1) Locales are a kind of space in which opens instead of points
are fundamental. (2) Sheaf semantics allows us to explore mathematical objects
from custom-tailored mathematical universes. (3) Without loss of generality,
any reduced ring is a field.
