Given two real, nonzero algebraic numbers a and b, with a > 0 (so that it excludes complex numbers), is there any named subset of the reals S such that (a^b) belongs to S forall a,b? I know it’s not all the reals since there should be countably many a^b’s, since a,b are also countable.
My mistake, in that case it’s not the closure what I mean. But then how are those kinds of sets called?
You could say something like “the image of exponentiation over…” to mean the set of values created by applying the function once, but it sounds slightly clunky.
Looks like there aren’t really very many sets of mostly transcendental numbers that have names. Computational numbers and periods are two of them, I’d guess that both probably contain your set, so you could compare with those to see where it gets you.