Definition:Language of Arithmetic

Definition
A language of arithmetic is a first-order signature consisting of:
 * the binary operation symbols: $+$ and $\cdot$
 * the unary function symbol: $s$
 * the binary relation symbol: $<$
 * the constant symbol: $0$

Standard Interpretation
The standard interpretation for this language is the set of integers with:
 * $+$: Integer addition
 * $\cdot$: Integer multiplication
 * $s$: the successor function
 * $<$: the usual strict ordering on the integers
 * $0$: interpreted as $0 \in \Z$

Comment
This is just one of many different signatures that could claim to be the language of arithmetic.