  We study the reverse mathematics of interval orders. We establish the logical
strength of the implications between various definitions of the notion of
interval order. We also consider the strength of different versions of the
characterization theorem for interval orders: a partial order is an interval
order if and only if it does not contain $2 \oplus 2$. We also study proper
interval orders and their characterization theorem: a partial order is a proper
interval order if and only if it contains neither $2 \oplus 2$ nor $3 \oplus
1$.
