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“Transfinite Induction” as a book category centers on works that develop and apply the method of extending mathematical induction to well-ordered infinite domains (ordinals), together with its companion technique, transfinite recursion. Titles in this category cover foundational set theory (ordinals and cardinals, well-orderings, ZF/ZFC), ordinal arithmetic and hierarchies, and advanced uses of transfinite methods across descriptive set theory, combinatorics, topology, model theory, and proof theory (including ordinal analysis and large cardinals). It spans rigorous textbooks, research monographs, and surveys, as well as historical and expository accounts tracing the technique from Cantor to contemporary logic. The emphasis is on reasoning about infinite, well-founded structures via ordinal stages—distinguishing it from broader “infinity” or general logic categories by its specific focus on induction and recursion beyond the finite.

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