I am honestly unconvinced on &quot;most of mathematics&quot; being just ZFC. You see this claim a lot, but when reading formal developments in mathematics I often see justifications involving &quot;small categories&quot; or statements which should hold in ZFC with &quot;enough universes a la Tarski&quot;.<p>But this is missing the point. There is a lot of active research work on program logics for reasoning about e.g., concurrent programs in weak memory models. You may be able to encode the model of something like Iris (<a href="http:&#x2F;&#x2F;plv.mpi-sws.org&#x2F;iris&#x2F;" rel="nofollow">http:&#x2F;&#x2F;plv.mpi-sws.org&#x2F;iris&#x2F;</a>) in TLA, but the challenge lies in doing this in a usable format...