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Turing degrees in Polish spaces and decomposability of Borel functions
[article]
2016
arXiv
pre-print
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. In fact it is essential to extend several prominent results in recursion theory (\eg the Shore-Slaman Join Theorem) to the setting of Polish spaces. As a by-product we give both positive and negative
arXiv:1410.1052v2
fatcat:rxyszurelbgg5l7p7awfojh5km