منابع مشابه
Forcing for IZF in Sheaf Toposes
In [Sco] D. Scott has shown how the interpretation of intuitionistic set theory IZF in presheaf toposes can be reformulated in a more concrete fashion à la forcing as known to set theorists. In this note we show how this can be adapted to the more general case of Grothendieck toposes dealt with abstractly in [Fou, Hay].
متن کاملSheaf toposes for realizability
We compare realizability models over partial combinatory algebras by embedding them into sheaf toposes. We then use the machinery of Grothendieck toposes and geometric morphisms to study the relationship between realizability models over different partial combinatory algebras. This research is part of the Logic of Types and Computation project at Carnegie Mellon University under the direction o...
متن کاملSheaves for predicative toposes
In this paper, we discuss the stability of predicative toposes under taking sheaves for an internal site. What is the most useful notion of a predicative topos has not been established yet, but we discuss sheafification for some candidates for that title. The results obtained here sharpen the results published by Moerdijk and Palmgren in [10] and [11]. We also propose a new axiom and show its u...
متن کاملCocomplete toposes whose exact completions are toposes
Let E be a cocomplete topos. We show that if the exact completion of E is a topos then every indecomposable object in E is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere–Schanuel characterization of Boolean presheaf toposes and Hofstra’s characterization of the locally connected Gro...
متن کاملNormalization of IZF with Replacement
IZF is a well investigated impredicative constructive version of Zermelo-Fraenkel set theory. Using set terms, we axiomatize IZF with Replacement, which we call IZFR, along with its intensional counterpart IZF − R. We define a typed lambda calculus λZ corresponding to proofs in IZF−R according to the Curry-Howard isomorphism principle. Using realizability for IZF−R, we show weak normalization o...
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ژورنال
عنوان ژورنال: gmj
سال: 2009
ISSN: 1572-9176,1072-947X
DOI: 10.1515/gmj.2009.203