Titlebook: Introduction to Axiomatic Set Theory; Gaisi Takeuti,Wilson M. Zaring Textbook 1982Latest edition Springer-Verlag New York Inc. 1982 Cardin

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Introduction,l and cardinal numbers was the culmination of three decades of research on number “aggregates.” Beginning with his paper on the denumer-ability of infinite sets,. published in 1874, Cantor had built a new theory of the infinite. In this theory a collection of objects, even an infinite collection, is conceived of as a single entity.

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Relational Closure and the Rank Function,ally interested in sets that are transitive. While there exist sets that are not transitive every set has a transitive extension. Indeed, every set has a smallest transitive extension which we call its transitive closure.

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The Fundamental Operations,s the union of a sequence of sets .., . ∈ On which were so defined that . ∈ ... iff there exists a wff .(.., ..,..., ..) having no free variables other than .., ..,..., .. and there exist ..,...,.. ∈ .. such that . = {.|..|= .(., ..,...,..)}.

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978-1-4613-8170-9Springer-Verlag New York Inc. 1982

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Introduction to Axiomatic Set Theory978-1-4613-8168-6Series ISSN 0072-5285 Series E-ISSN 2197-5612

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https://doi.org/10.1007/978-1-4613-8168-6Cardinal number; arithmetic; axiom of choice; bridge; class; development; forcing; object; set; set theory; ti

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