There are many ways to express that a sequence converges. They range from the most explicit but least uniform---a rate of convergence; to the moderately explicit and moderately uniform---a bound on the number of jumps by epsilon; to the least explicit but most uniform---a bound of metastable convergence (which I will define in this talk).

Using proof theory, Kolhenbach showed that uniform metastable bounds can be computably extracted from the proof of a convergence theorem. Using model theory, Avigad and Iovino showed that metastable bounds of a convergence theorem are always uniform---but their methods do not provide a way to compute the bounds. Using computable analysis and computable model theory, I show that not only are the bounds always uniform, but they can computed from the statement of the theorem alone (without regards to the proof).