The Buchholz hydra is a concept from set theory and mathematical logic, particularly within the study of large cardinals and the foundations of mathematics. It was introduced by the mathematician Wolfgang Buchholz as a part of his work on proof theory and the analysis of formal systems. The Buchholz hydra is often discussed in the context of certain types of ordinal notations, especially in connection with ordinal collapsing functions and strong axioms of infinity.
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