Abstract: Following the fundamental work of Friedman-Stanley and Hjorth-Kechris, it is now well-known that descriptive set theory provides a framework for measuring the relative complexity of many naturally occurring classification problems. It is less well-known that descriptive set theory also provides a framework for explaining the inevitable non-uniformity of many classical constructions in mathematics. In this talk, I will illustrate this point by considering two constructions from combinatorial group theory related to the word problem for finitely generated groups and the Higman-Neumann-Neumann Embedding Theorem.
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