I'm taking a look at Enderton's A Mathematical Introduction To Logic, and at first glance it looks to me like he is assuming at the outset the natural numbers along with induction.
The reason I think this is because at the outset he defines an $(n+1)$-tuple as an ordered pair of an $n$-tuple and an additional value, then proceeds to use an induction argument to show a uniqueness lemma (Lemma 0A).
Question: Do I understand correctly that he is at the outset assuming that we have the naturals and can do ordinary induction on them? (I noticed that he wrote this book before his set theory book.)
Thanks.
