Wang writes: "The originally intended, or standard, interpretation takes the ordinary nonnegative integers $\{0, 1, 2, \ldots \}$ as the domain, the symbols $0$ and $1$ as denoting zero and one, and the symbols $+$ and $\cdot$ as standing for ordinary addition and multiplication.'' This comment is found in section "Truth definition of the given language'' of article "Metalogic'' in Encyclopedia Britannica online at http://www.britannica.com/topic/metalogic

Is there a source for such a characterisation or another characterisation of the Intended Interpretation in a more traditional publication in a refereed journal or book?

Note 1. I am asking for a published source for the characterisation provided by the renouned logician Hao Wang, establishing a connection between a standard $\mathbb{N}$ on the one hand and what he seems to take to be the ordinary numbers with "ordinary addition and multiplication", on the other.

Note 2. The historical comments by user Francois Dorais concerning Frege, Peano, and Dedekind are interesting but I think inconclusive so far. It would be nice to get a clarification.