Regarding, re.
Abbreviation of "recursively enumerable"; the class of decision problems for which a 'yes' answer can be verified by a Turing machine in a finite amount of time.
Arriving upon or on top of (speaking of a physical or metaphorical movement).
Being an onto function with a codomain of (see below).
Aware of.
Assuming each of the values in its codomain; having its range equal to its codomain.