Complexity of self-correcting algorithms for two sorting problems

For a standard sorting problem for an $n$-element set we obtain an algorithm, optimal with respect to order, that corrects up to $k(n)$ incorrect comparisons of elements of a sortable set. We show that this algorithm is asymptotically optimal when $k=o(\log n)$. We also obtain a self-correcting algorithm, optimal with respect to order, for a sorting problem of a set that is isomorphic to a Boolean algebra.