THE USE OF COMPLEXITY HIERARCHIES IN DESCRIPTIVE SET THEORY AND AUTOMATA THEORY

ALESSANDRO ANDRETTA, RICCARDO CAMERLO
2005 TASK Quarterly  
The concept of a reduction between subsets of a given space is described, giving rise to various complexity hierarchies, studied both in descriptive set theory and in automata theory. We discuss in particular the Wadge and Lipschitz hierarchies for subsets of the Baire and Cantor spaces and the hierarchy of Borel reducibility for finitary relations on standard Borel spaces. The notions of Wadge and Lipschitz reductions are related to corresponding perfect information games.
doaj:0f44ec1146c94f169c29107949943a3f fatcat:dxvm7dqd4ncdvmbdirup4o7xca