Zermelo-Fraenkel Set Theory (ZF) is a foundational system for mathematics that formalizes the concept of sets and their relationships. It consists of a collection of axioms that define how sets can be constructed and manipulated, providing a rigorous framework for dealing with infinite sets and operations. This theory plays a critical role in proof-theoretic reductions and ordinal analysis by offering a structured way to explore the properties of mathematical structures and their proofs.
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