Turing degrees in Polish spaces and decomposability of Borel functions

• Main Authors: Gregoriades, Vassillos, Kihara, Takayuki, Ng, Meng Keng
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Countably Continuous Function; Jayne–Rogers Theorem
• Online Access: https://hdl.handle.net/10356/155095
• Institution: Nanyang Technological University

We give a partial answer to an important open problem in descriptive set theory, the Decomposability Conjecture for Borel functions on an analytic subset of a Polish space to a separable metrizable space. Our techniques employ deep results from effective descriptive set theory and recursion theory....