Finiteness and Computation in Toposes
نویسندگان
چکیده
منابع مشابه
Finiteness and Computation in Toposes
Some notions in mathematics can be considered relative. Relative is a term used to denote when the variation in the position of an observer implies variation in properties or measures on the observed object. We know, from Skolem theorem, that there are first-order models where R is countable and some where it is not. This fact depends on the position of the observer and on the instrument/langua...
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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...
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Toposes and quasi-toposes have been shown to be useful in mathematics, logic and computer science. Because of this, it is important to understand the different ways in which they can be constructed. Realizability toposes and presheaf toposes are two important classes of toposes. All of the former and many of the latter arise by adding “good” quotients of equivalence relations to a simple catego...
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In [2], Barr and Diaconescu characterized those Grothendieck toposes 8 for which the inverse image, A, of the geometric morphism r: 8 + Yet, is logical. It was shown (among other things) that this happens precisely when the lattice of subobjects of every object of 8 is a complete atomic boolean algebra. Toposes satisfying this property are called atomic. These results were relativised to the ca...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2016
ISSN: 2075-2180
DOI: 10.4204/eptcs.204.6