Ackermann's set theory equals ZF
نویسندگان
چکیده
منابع مشابه
Model of ZF Set Theory
The goal of this article is to construct a language of the ZF set theory and to develop a notational and conceptual base which facilitates a convenient usage of the language. and 2] provide the notation and terminology for this paper. For simplicity we adopt the following rules: k, n denote natural numbers, D denotes a non empty set, a is arbitrary, and p, q denote nite sequences of elements of...
متن کاملA Model of ZF Set Theory Language
The articles [5], [6], [3], [4], [1], and [2] provide the terminology and notation for this paper. For simplicity we adopt the following convention: k, n will have the type Nat; D will have the type DOMAIN; a will have the type Any; p, q will have the type FinSequence of NAT. The constant VAR has the type SUBDOMAIN of NAT, and is defined by it = { k : 5 ≤ k }. The following proposition is true ...
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Most general purpose proof assistants support versions of typed higher order logic. Experience has shown that these logics are capable of representing most of the mathematical models needed in Computer Science. However, perhaps there exist applications where ZF-style set theory is more natural, or even necessary. Examples may include Scott’s classical inverse-limit construction of a model of th...
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We present a system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On the one hand, this system is a common weakening of Zermelo-Fraenkel set theory ZF , the positive set theory GPK∞ and the theory of hyperuniverses. On the other hand, it retains most of the expressiveness of these theories and has the same consistency strength as ZF . W...
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A special final coalgebra theorem, in the style of Aczel (1988), is proved within standard Zermelo-Fraenkel set theory. Aczel’s Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel’s solution and substitution lemma...
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1970
ISSN: 0003-4843
DOI: 10.1016/0003-4843(70)90011-2