Ph.D XLI

Supervisor: Vincenzo Dimonte

Room: Rizzi A2 104

Mail: pisciotta.federico@spes.uniud.it

Research Project

Aspect of Generalized Descriptive Set Theory

This project explores the extension of classical descriptive set theory from the Baire space ω^ω and the Cantor space 2^ω to generalized spaces , focusing on singular cardinals of countable cofinality. We examine which fundamental notions from the classical case like Borel hierarchies, definability, and regularity properties persist or fail in this generalized context. The project highlights the new phenomena arising from the lack of compactness  at singular cardinals. We analyze how combinatorial principles governing the classical theory must be modified or replaced. We also analyze the interaction between large cardinal assumptions and determinacy-like phenomena in this context.