An effective Stone duality is preserved under Z-c.e. presentations, allowing every degree spectrum of a countable algebraic structure to be realized as the degree spectrum of a topological space with base and the construction of spaces with precisely N computable copies.
Wehner,Enumerations, countable structures and Turing degrees, Proceedings of the American Mathematical Society126, no
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An effective version of the Stone duality
An effective Stone duality is preserved under Z-c.e. presentations, allowing every degree spectrum of a countable algebraic structure to be realized as the degree spectrum of a topological space with base and the construction of spaces with precisely N computable copies.