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In this chapter, we shall present and discuss the axioms of Zermelo-Fraenkel Set Theory including the Axiom of Choice, denoted ZFC. It will turn out that within this axiom system, we can develop all of first-order mathematics, and therefore, the axiom system ZFC serves as a foundation of mathematics.

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The Axioms of Set Theory (ZFC)

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  • 发表日期：

    2025年

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  • Lorenz Halbeisen,
  • Regula Krapf

摘要

In this chapter, we shall present and discuss the axioms of Zermelo-Fraenkel Set Theory including the Axiom of Choice, denoted ZFC. It will turn out that within this axiom system, we can develop all of first-order mathematics, and therefore, the axiom system ZFC serves as a foundation of mathematics.