In this paper we show that using implicative algebras one can produce models of set theory generalizing Heyting/Boolean-valued models and realizability models of (I)ZF, both in intuitionistic and classical logic. This has as consequence that any topos which is obtained from a Set-based tripos as the result of the tripos-to-topos construction hosts a model of intuitionistic or classical set theory, provided a large enough strongly inaccessible cardinal exists.

翻译：本文证明，利用蕴涵代数可以构建集合论的模型，这些模型统一推广了直觉主义与经典逻辑中（I）ZF的Heyting/布尔值模型和可实现性模型。由此得出推论：只要存在足够大的强不可达基数，任何通过tripos到topos构造从基于集合的tripos得到的topos，都能承载直觉主义或经典集合论的模型。