Hilbert's nullstellensatz revisited

Using sheaf semantics, Hilbert's Nullstellensatz is shown to be valid for geometric fields in sheaves over Boolean spaces. From this result, the analogue of the Nullstellensatz for regular rings (first proved in [9]) is easily recovered. Some previous work is then summarized, in which Hilbert's Nullstellensatz is shown to be valid in an arbitrary topos. The result of [9] may be recovered from this as well.