  In the study of free arrangements, the most useful result to construct/check
free arrangements is the addition-deletion theorem. Recently, the multiple
version of the addition theorem is proved, called the multiple addition theorem
(MAT) to prove the ideal-free theorem. The aim of this article is to give the
deletion version of MAT, the multiple deletion theorem (MDT). Also, we can
generalize MAT from the viewpoint of our new proof. Moreover, we introduce
their restriction version, a multiple restriction theorem (MRT). Applications
of them including the combinatorial freeness of the extended Catalan
arrangements are given.
