One more recursive-theoretic characterization of the Topological Vaught Conjecture

TL;DR

This paper provides a recursive-theoretic characterization of the Topological Vaught Conjecture within ZF set theory, revisiting the Borel nature of orbits in Polish G-spaces to deepen understanding.

Contribution

It introduces a new recursive-theoretic perspective on the Topological Vaught Conjecture, expanding the theoretical framework without relying on the Axiom of Choice.

Findings

Characterization of the conjecture in ZF

Revisiting Borel sets in Polish G-spaces

New insights into orbit structures

Abstract

We prove in ZF a recursive-theoretic characterization of the Topological Vaught Conjecture by revisiting the fact that orbits in Polish $G$-spaces are Borel sets.