algorithm for > determining, "spam".
I think we all can agree that if repeated "3"'s and repeated "1"'s are
spamming, then also repeated "4" = 3 + 1 is spamming, and so forth for all the
required number theoretic axioms. Gödel's incompleteness theorem then states
that there is no such algorithm, which outputs "true" for every string x which
is spam. Also with the same argument we get that being a spam is not finitely
axiomatizable, so what you're asking is impossible to do.