This paper presents a systematic investigation of the basic axioms of the theory of E0L forms, in particular it continues the research from Rozenberg and Verraedt. Three new interpretation mechanisms—fixed, terminal fixed and nonterminal fixed interpretations—are introduced and extensively studied. When compared with terminal invariant and nonterminal invariant interpretations from Rozenberg and Verraedt these interpretations constitute a natural “next step” towards increasing the similarity of the “master” E0L form with its interpretations. In particular it is shown that each (ordinary) E0L family is a nonterminal fixed E0L family. It is also proved that for each of the new defined interpretation mechanisms the form equivalence problem is undecidable.
