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axiom of power set
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axiom of power set

set theory
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The axiom of power set is a fundamental principle in Zermelo-Fraenkel set theory (ZF), a foundational system for mathematics. It asserts that for any given set, there exists another set containing all of its possible subsets. This axiom is crucial for constructing more complex sets from existing ones and is essential for developing concepts like transfinite induction and ordinal arithmetic. The Zermelo-Fraenkel axioms, including the axiom of power set, were developed to avoid paradoxes found in naive set theory by restricting the types of sets that can be formed.1234

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5 Britannica Sources
  1. set theory - Axiom for eliminating infinite descending species
  2. set theory - Axioms for compounding sets
  3. set theory - Schema for transfinite induction and ordinal arithmetic
  4. history of logic - Zermelo-Fraenkel set theory (ZF)
  5. set theory - Present status of axiomatic set theory

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