  Pseudo $MV$-algebras are a non-commutative generalization of $MV$-algebras.
The main purpose of the paper is to introduce and investigate orthocomplete
pseudo $MV$-algebras. We use the concepts of projectable pseudo $MV$-algebras
and large pseudo $MV$-subalgebras to introduce orthocomplete pseudo
$MV$-algebras. Then we apply a generalization of the Mundici's functor to an
orthocompletion of an representable $\ell$-group to prove that each
representable pseudo $MV$-algebra has an orthocompletion. In particular, our
results are valid also for $MV$-algebras.
