Recursive functions and existentially closed structures

Emil Jeřábek

doi:10.1142/s0219061320500026

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arXiv · 1710.09864

Recursive functions and existentially closed structures

Emil Jeřábek

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Abstract

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$ does not interpret Robinson's theory $R$. To this end, we borrow tools from model theory--specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of $\exists\forall$ theories interpretable in existential theories in the process.

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BibTeX RIS

Emil Jeřábek. 2017-10-26. Recursive functions and existentially closed structures. https://doi.org/10.1142/s0219061320500026

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