 We want to find a totally recursive function "f" with the property that
for all "n" and for any "n"-length sequence of natural numbers formula_1, there exists an appropriate natural number "a", called the Gödel number of the sequence, such that for all "i" where formula_2, formula_3.There are effective functions which can retrieve each member of the original sequence from a Gödel number of the sequence.Moreover, we can define some of them in a constructive way, so we can go well beyond mere proofs of existence.