I am self-learning about formal languages. I learned that the family of the regular languages can be defined inductively, in terms of the operations they are closed under (namely the smallest fix-point). This definition doesn't rely on regular grammars or finite state machines.I wonder which other families of formal languages can be defined inductively; in particular, I am interested in the classic classes of the Chomsky hierarchy but also the (semi-)decidable languages.
Which language families admit inductive definitions?
formal languages;reference request