How do you represent an r.e. complexity class with a list of TMs?


In this book ‘Theory of computation’ By Dexter Kozen on page 313,exercise 127 he says “A set of total recursive functions is recursively enumerable (r.e.) if there exists an r.e. set of indices representing all and only functions in the set. For example, the complexity class P is r.e., because we can represent it by an r.e. list of TMs with polynomial-time clocks.” How do you do what he is talking about for any collection of languages that is r.e.? How do you represent an r.e. complexity class with a list of TMs? What is an example of an enumerator that does this for any r.e. class C?