The Skolem-Löwenheim theorem in toposes. II (Q1068081)

This paper is a continuation of the author's earlier investigations [ibid. 42, 461-475 (1983; Zbl 0561.03021)]. The main result here is that, in a suitable class of Grothendieck toposes, the usual universal and existential quantifiers satisfy the ''reducibility'' conditions introduced in the previous paper for generalized quantifiers. As a corollary, the author obtains results of Skolem-Löwenheim type for Kripke models and for dynamic models \((=models\) in categories of M-sets, where M is a monoid).