  For integers $k\ge 2$ and $N\ge 2k+1$ there are $k!2^k$ canonical orderings
of the edges of the complete $k$-uniform hypergraph with vertex set $[N] =
\{1,2,\dots, N\}$. These are exactly the orderings with the property that any
two subsets $A, B\subseteq [N]$ of the same size induce isomorphic
suborderings. We study the associated canonisation problem to estimate, given
$k$ and $n$, the least integer $N$ such that no matter how the $k$-subsets of
$[N]$ are ordered there always exists an $n$-element set $X\subseteq [N]$ whose
$k$-subsets are ordered canonically. For fixed $k$ we prove lower and upper
bounds on these numbers that are $k$ times iterated exponential in a polynomial
of $n$.
