I am making a scheme that respresents some closure properties (union, intersection, complement and concatenation) for regular languages, context-free languages, decidable languages and RE languages. Below you can see my scheme.
I am trying to find all possible internal closure properties of these different languages that will always be valid. E.g., I know that $$\text{Regular language } \cup \text{ CFL } = \text{ CFL } $$
$$\text{Regular language } \cap \text{ CFL } = \text{ CFL } $$ $$\text{Regular language } ^* \text{ CFL } = \text{ CFL } $$
What other internal properties are there between these languages?