Successor structure
= Successor structure
{title2=$(\mathbb N,s,0)$}
The standard successor structure has the <natural numbers> as domain, the <successor function> $s(n)=n+1$, and the named element zero. Its complete <first-order theory> is the <theory of successor>. Without addition, multiplication, or order, elements outside the zero-generated component are possible in other models of the same <complete theory>.