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- Associativity of ordinal addition
- Coded relative constructible stage
- Countable fixed point of a normal ordinal function
- Gentzen ordinal reduction for arithmetic
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- Row-and-column enumeration of an ordinal square
- Stage histories appear below every limit constructible level
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Transfinite induction is a generalization of mathematical induction that applies to well-ordered sets, particularly those that are not necessarily finite. It allows statements or properties about all ordinal numbers to be proven by establishing a basis and then using the principle of induction over transfinite ordinals.