Further Results on Hierarchies of Canonic Systems

Abstract

This thesis outlines a new way of presenting the theory of canonic systems, including a distinction (for mathodic reasons) between simple canonic systems and general canonic systems, and proves a series of results on hierarchies of canonic systems. After a brief summary of Doyle's results on a partial hierarchy of canonic systems, a new hierarchy is developed (Chapter II) which relates the general canonic systems not only to all 4 types of formal grammars defined by Chomsky but also to any class shown (Chapter III) that all attempts to define a mathematical system which exactly corresponds to the recursive sets are necessarily fruitless.