Simpson's systems of second order arithmetic turn out to be five in number; to simplify notation let's denote them A, B, C, D, E. What seems to be an empirical observation is that most theorems in classical analysis "revert" to one of the five systems, meaning of course that they are equivalent (over A = RCA$_0$) to the defining property of the system.

Can this empirical fact be made into a theorem somehow? I am thinking of something along the lines of the classification of finite simple groups, where a consequence of the classification is the observation that almost all groups fall into four specific infinite families (the latter observation is of course a precise mathematical statement rather than merely an empirical observation).

Simpson's systems of second order arithmetic turn out to be five in number; to simplify notation let's denote them A, B, C, D, E. What seems to be an empirical observation is that most theorems in classical analysis "revert" to one of the five systems, meaning of course that they are equivalent (over A = RCA$_0$) to the defining property of the system.

Can this empirical fact be made into a theorem somehow? I am thinking of something along the lines of the classification of finite simple groups, where a consequence of the classification is the observation that almost all groups fall into four specific infinite families (the latter observation is of course a precise mathematical statement rather than merely an empirical observation).