Control sets on linear grammars

Control sets on linear grammars are used to define a generalization of the metalinear hierarchy within the context free languages. The families introduced are defined inductively by controlling labeled linear grammars with languages in one family, to yield languages in the next larger family, starting the induction with the metalinear families. The essential properties of these families are analogous to those of the context free family. In particular, decidability properties are the same and on one symbol alphabets member languages are regular. These are consequences of entirely new pumping results which provide a classification within the context sensitive languages, finer than the classical one.