The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver ([19]) and Harrington-Kechris-Louveau ([5]) show that with respect to Borel reducibility, any Borel equivalence relation strictly above equality on ω is above equality on P(ω), the power set of ω, and any Borel equivalence relation strictly ...

We introduce and study the notion of functorial Borel complexity for Polish groupoids. Such a notion aims at measuring the complexity of classifying the objects of a category in a constructive and functorial way. In the particular case of principal groupoids such a notion coincide with the usual Borel complexity of equivalence relations. Our main result is that on one hand for Polish groupoids ...

Event shapes are classical tools for the determination of strong coupling and study hadronization effects in electron-positron annihilation. In context analytical studies, corrections take form power-suppressed contributions to cross-section, which can be extracted from perturbative ambiguity Borel-resummed distributions. We propose a simplified version well-established method Dressed Gluon Exp...

We consider a descriptive version of Kakutani equivalence for Borel automorphisms of Polish spaces. Answering a question of Nadkarni, we show that up to this notion, there are exactly two Borel automorphisms: those which are smooth, and those which are not. Using this, we classify all Borel R-flows up to C∞ time-change isomorphism. We then extend the notion of Kakutani equivalence to all (not n...