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Recursive functions and existentially closed structures
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 in which all partially recursive functions are
representable, yet does not interpret Robinson's theory . 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
theories interpretable in existential theories in the process.Comment: 42 pages; to appear in Journal of Mathematical Logi