A Brief Introduction to Zfc
نویسنده
چکیده
We present a basic axiomatic development of Zermelo-Fraenkel and Choice set theory, commonly abbreviated ZFC. This paper is aimed in particular at students of mathematics who are familiar with set theory from a “naive” perspective, and are interested in the underlying axiomatic development. We will quickly review some basic concepts of set theory, before focusing on the set theoretic definition of the natural numbers, and the equivalence of the axiom of choice, Zorn’s lemma, and well ordering principle.
منابع مشابه
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In this paper, we study the union axiom of ZFC. After a brief introduction, we sketch a proof of the folklore result that union is independent of the other axioms of ZFC. In the third section, we prove some results in the theory T:= ZFC minus union. Finally, we show that the consistency of T plus the existence of an inaccessible cardinal proves the consistency of ZFC.
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