Richard Kaye works on mathematical logic and arithmetic model theory. His exposition of Tennenbaum's theorem studies why countable nonstandard arithmetic cannot have an ordinary computable presentation with computable operations.[ref]
Tennenbaum’s Theorem for Models of Arithmetic by Richard Kaye (2006). Author byline and theorem exposition
The proof encodes a standard nonrecursive set inside a nonstandard model, using recursively inseparable sets and overspill. If the model's arithmetic were computable in the required way, the coded set could be recovered algorithmically, giving a contradiction. Kaye's account makes the interaction between model theory and computability theory explicit.[ref]
Tennenbaum’s Theorem for Models of Arithmetic by Richard Kaye (2006). Construction preceding Theorem 2.8
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