On computable aspects of algebraic and definable closure

Nathanael Ackerman; Cameron Freer; Rehana Patel

doi:10.1093/logcom/exaa070

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arXiv · 2101.11849

On computable aspects of algebraic and definable closure

Nathanael Ackerman·Cameron Freer·Rehana Patel

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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 $\Sigma^0_{n+2}$ sets. We further show that these bounds are tight.

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BibTeX RIS

Nathanael Ackerman, Cameron Freer, Rehana Patel. 2021-01-28. On computable aspects of algebraic and definable closure. https://doi.org/10.1093/logcom/exaa070

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