منابع مشابه
Classifying topoi and the axiom of infinity
Let 6 e be an elementary topos. The axiom of infinity, asserting that 5 e has a natural numbers object, is shown to be necessary-sufficiency has long been k n o w n f o r the existence of an object-classifying topos over 5 e. In the known constructions [1, 4, 6] of classifying topoi for geometric theories, it is always assumed that the base topos fie satisfies the axiom of infinity. The purpose...
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Let {Σα}α<ω1 , where ω1 is the first non-countable ordinal, denote the Borel hierarchy of subsets of the Cantor space 2. As usual, Πα denotes the dual class for Σα while ∆ 0 α = Σ 0 α ∩Πα — the corresponding ambiguous class. Let B = ∪α<ω1Σα denote the class of all Borel sets. The levels of Borel hierarchy, as well as many other classes of interest for descriptive set theory, may be defined by m...
متن کاملClassifying n-Input Boolean Functions
This paper discusses the classification of n-input Boolean functions. The concept of P and NPN equivalence classes is used to classify n-input functions. This way, the set of n-input functions is classified according to three criteria: the number of functions, the number of P classes and the number of NPN classes. The meaning of these criteria is discussed through some affirmations relating the...
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A Petri net model is referred to as Boolean if the only possible markings are sets, i.e., places are marked or not without further quantification; moreover, also the enabling conditions and firing rule are based on this principle of set-based token arithmetic. Elementary Net systems are an example of a class of Boolean nets, and so are the recently introduced set-nets. In our investigation of t...
متن کاملSheaf representation for topoi
It is shown that every (small) topos is equivalent to the category of global sections of a sheaf of so-called hyperlocal topoi, improving on a result of Lambek & Moerdijk. It follows that every boolean topos is equivalent to the global sections of a sheaf of well-pointed topoi. Completeness theorems for higher-order logic result as corollaries. The main result of this paper is the following. Th...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1983
ISSN: 0022-4049
DOI: 10.1016/0022-4049(83)90069-5