  We axiomatise the theory of $(\infty,n)$-categories. We prove that the space
of theories of $(\infty,n)$-categories is a $B(\mathbb{Z}/2)^n$. We prove that
Rezk's complete Segal $\Theta_n$-spaces, Simpson and Tamsamani's Segal
$n$-categories, the first author's $n$-fold complete Segal spaces, Kan and the
first author's $n$-relative categories, and complete Segal space objects in any
model of $(\infty,n-1)$-categories all satisfy our axioms. Consequently, these
theories are all equivalent in a manner that is unique up to the action of
$(\mathbb{Z}/2)^n$.
