[yyxbmjqp] larger than algebraic

algebraic numbers are closed under a bunch of arithmetic operations, but not under exponentiation: Gelfond-Schneider theorem.  this is not too surprising: going from integers to rationals to algebraic each time involves permits more operations.

this suggests a larger set of numbers, a superset of algebraic, that is also closed under exponentiation.  does this set have a name?  how can it be precisely defined?

perhaps plus, minus, times, divide, RootOf, exp, and log.  (arbitrary exponentiation can be written in terms of e^x and natural logarithm.) subtraction, division, and logarithm are redundant with RootOf.  maybe add Lambert W, though that is also redundant with RootOf.  we definitely need to keep RootOf because there are algebraic numbers, solutions to quintics and higher, not reachable without it.  note that RootOf for algebraic numbers was restricted to polynomials, but this RootOf can handle a larger class of equations.  (should it?)

this set is almost certainly a strict subset of the real numbers (or the complex numbers) because this set is computable, and there almost certainly exist real numbers that are not computable.  can one construct a computable number not in this set?  there are probably many easy examples, numbers known only by infinite series.  but it might be difficult to prove.

pi is a number in this set, because pi is famously RootOf(exp(i*pi)+1 = 0).  but pi might be special because it is tied into logarithm being multivalued.