	All arithmetical subsets of ω and relations on ω belong to L (because the arithmetic definition gives one in L). Conversely, any subset of ω belonging to L is arithmetical (because elements of L can be coded by natural numbers in such a way that ∈ is definable, i.e., arithmetic). On the other hand, L already contains certain non-arithmetical subsets of ω, such as the set of (natural numbers coding) true arithmetical statements (this can be defined from L so it is in L).