Zermelo-Fraenkel Axioms | 私立大學五星教授網

Formally, ZFC is a one-sorted theory in first-order logic. Equality is treated as a primitive logical symbol and the signature has a single primitive non- ...

策梅洛-弗蘭克爾集合論（英語：Zermelo-Fraenkel Set Theory），是數學基礎中最常用的一階公理化集合論。含選擇公理時常簡寫為ZFC，不含選擇公理的則簡寫為ZF。

This axiom asserts that when sets -(x-) and -(y-) have the same members, they are the same set. The next axiom asserts the existence of the empty set: Null Set:

ZFC, or Zermelo-Fraenkel set theory, is an axiomatic system used to formally define set theory (and thus mathematics in general). Specifically, ZFC is a ...

In this chapter, we shall present and discuss the axioms of Zermelo-Fraenkel Set. Theory including the Axiom of Choice, denoted ZFC.

由 EW Weisstein 著作 · 2003 · 被引用 2 次 — The system of axioms 1-8 is called Zermelo-Fraenkel set theory, denoted ZF. The system of axioms 1-8 minus the axiom of replacement (i.e., axioms 1-6 plus 8) ...

由 T LIAN 著作 · 2011 · 被引用 5 次 — As we will show, ZF set theory is a highly versatile tool in defining mathematical foundations as well as exploring deeper topics such as ...

2023年5月9日 — ZFC ZFC is a simply typed first-order material set theory, with a single type V V called the cumulative hierarchy and a binary membership ...

ZFC set theory is strongly believed to be consistent, although ZFC set theory ... A single set theory is therefore a theory employing the language of set theory.