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：本文表明，利用蕴涵代数可以构造集合论的模型，这些模型推广了（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。由此可得，在存在足够大的强不可达基数的前提下，任何基于集合的tripos通过tripos到topos构造得到的topos都承载着直觉主义或经典集合论的模型。