A large algebraically closed field

A sequence is called an R.R.S. sequence if, roughly speaking, it is generated by some member of a set of recurrence formulas over the field $Q(i)$ which involves only rational operations. It is proved that the set of limits of all convergent R.R.S. sequences forms a countable algebraically closed field. Moreover, the field is shown to contain all numbers of the form ${e^\alpha }$, where $\alpha$ is an algebraic number.