A recursion theoretic characterization of the Topological Vaught Conjecture in the Zermelo-Fraenkel set theory: A recursion theoretic characterization of the Topological Vaught Conjecture in ZF

We prove a recursion theoretic characterization of the Topological Vaught Conjecture in the Zermelo-Fraenkel set theory by using tools from effective descriptive set theory and by revisiting the result of Miller that orbits in Polish G-spaces are Borel sets. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim