Consider a language $L$ with $<0,1,S>$, where $S$ is the successor function.
Show that there are only $\aleph_0$ many countable models of Th$(\mathbb{N})$, under $L$.
This is one of the practice question in the book by Richard Kaye, Models of peano arithmetics.
Chapter 1, question 1.3.
I'm honestly quite stuck and do not know how to begin.
Any help or insight is deeply appreciated.
Cheers