Abstract
We consider computability-theoretic aspects of the algebraic and definable closure operations for formulas. We show that for \(\varphi \) a Boolean combination of \(\varSigma _n\)-formulas and in a given computable structure, the set of parameters for which the closure of \(\varphi \) is finite is \(\varSigma ^0_{n+2}\), and the set of parameters for which the closure is a singleton is \(\varDelta ^0_{n+2}\). In addition, we construct examples witnessing that these bounds are tight.
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Ackerman, N., Freer, C., Patel, R. (2020). Computability of Algebraic and Definable Closure. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2020. Lecture Notes in Computer Science(), vol 11972. Springer, Cham. https://doi.org/10.1007/978-3-030-36755-8_1
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DOI: https://doi.org/10.1007/978-3-030-36755-8_1
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