Submission date: 28 January 2021

Abstract:

We investigate the computability of algebraic closure and definable closure with respect to a collection of formulas. We show that for a computable collection of formulas of quantifier rank at most n, in any given computable structure, both algebraic and definable closure with respect to that collection are Σ^0_{n+2} sets. We further show that these bounds are tight.

Mathematics Subject Classification:

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Full text arXiv 2101.11849: pdf, ps.