Strong De Morgan's law and the spectrum of a commutative ring (Q2266766)

The ''strong De Morgan's law'' in a topos is the assertion that the object of truth-values is (internally) linearly ordered. In Lect. Notes Math. 753, 479-491 (1979; Zbl 0445.03041), the reviewer showed that this condition holds in the topos of sheaves on a topological space X iff every closed suspace of X is extremally disconnected. The main result of this paper is that the condition holds for the spectrum of a Noetherian domain R iff R is a Dedekind domain (an example is given to show that the Noetherian condition cannot be dropped).