Tennenbaum's theorem states that PA does not admit any

computable model other than the "usual natural numbers" (this is called

the standard 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 symbols") 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.