Layers over minimal logic

We introduce a classification of extensions of Johansson's minimal logic J that extends the classification of superintuitionistic logics proposed by T. Hosoi. It is proved that the layer number of any finitely axiomatizable logic is effectively computable. Every layer over J has a least logic. It is stated that each layer has finitely many maximal logics, and minimal and maximal logics of all layers are recognizable over J.