Thanks for your reading,

A set S is recursively enumerable if one can write a program such that, once the program is launched, it will print a list of elements of S and, for all elements s ∈ S , the program will eventually print out the element s .

Which of the following are recursively enumerable sets?

A. N (where N means nature numbers)

B. N×N (where N means nature numbers)

C. The power set P(N) of subsets of N.

D. The set of formal propositions.

E. The set of rational numbers Q .

The answer is "A,B,D,E"

I'm confused about the choice "D. The set of formal propositions"

Thanks indeed!

PS: "formal propositions" means "the proposition made up of specific symbol rather than English words" (for instance, ョx∈N, x<5)

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I have already posted this on stack-overflow by my mistake but get some answer:

Reference: <https://stackoverflow.com/questions/21499731/why-is-the-set-of-formal-propositions-enumerable> 

"Formal propositions are recursively enumerable only if we assume that we are only interested in the "writable" ones (such, which have finite length in terms of symbols from some finite/enumerable vocablurary).

In such case we can write the program, which given pair (A,B) writes A'th proposition of length B, and than use our program for writing down NxN to write them down. The existance of the first program is based on assumption that: we use some finite set of symbols to write them down (or at least enumerable); our propositions are finite in terms of length (our program has to be able to print them out)."

==> If I can do with this technique, why "C. The power set P(N) of subsets of N." is not the answer to this question?