A NEW FORMALIZATION OF FEFERMAN’S SYSTEM OF FUNCTIONS AND CLASSES AND ITS RELATION TO FREGE STRUCTURE
Susumu Hayashi, Satoshi Kobayashi · International Journal of Foundations of Computer Science · 1995
A new axiomatization of Feferman’s systems of functions and classes1,2 is given. The new axiomatization has a finite number of class constructors resembling the proposition constructors of Frege structure by Aczel.3 Aczel wrote “It appears that from the technical point of view the two approaches (Feferman’s system and Frege structure) run parallel to each other in the sense that any technical result for one approach can be reconstructed for the other”.3 By the aid of the new axiomatization, Aczel’s observation becomes so evident. It is now straightforward to give a mutual interpretation between our formulation and a first order theory of Frege structure, which improve results by Beeson in Ref. 4.