Ordinal induction is a proof technique that extends the principles of mathematical induction to ordinal numbers, allowing one to prove properties of well-ordered sets. It relies on the concept of ordinals as a way to generalize and organize the process of induction, particularly in contexts where standard induction is insufficient. This method is essential in proof-theoretic reductions and ordinal analysis, as it facilitates the exploration of transfinite proofs and the structure of formal systems.
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