Tennenbaum's theorem states that PA does not admit any nonstandard computable model. In 2022, Fedor Pakhomov proved that this theorem is fragile in regards to how PA is expressed, by constructing a theory that is definitionally equivalent to PA (roughly: “it’s PA but with a different choice of signature”) for which there is a computable nonstandard model. I will introduce the audience to this result and, time allowing, present the way in which we have been able to improve on Pakhomov's original construction and some remaining open questions.