A NEW FORMALIZATION OF FEFERMAN’S SYSTEM OF FUNCTIONS AND CLASSES AND ITS RELATION TO FREGE STRUCTURE

Author:

HAYASHI SUSUMU1,KOBAYASHI SATOSHI2

Affiliation:

1. Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Ohtsu, Shiga, Japan

2. Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Ohtsu, Shiga, Japan

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Science (miscellaneous)

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Theories of Frege structure equivalent to Feferman's system T0;Annals of Pure and Applied Logic;2025-01

2. THE UNIVERSAL SET AND DIAGONALIZATION IN FREGE STRUCTURES;The Review of Symbolic Logic;2011-06

3. Universes over Frege structures;Annals of Pure and Applied Logic;2003-02

4. MARTIN-LÖF'S TYPE THEORY AS AN OPEN-ENDED FRAMEWORK;International Journal of Foundations of Computer Science;2001-02

5. Frege structures for partial applicative theories;Journal of Logic and Computation;1999-10-01

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