Inconsistency of GPK + AFA

✍ Scribed by Olivier Esser

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 233 KB
• Volume: 42
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19960420109

✦ Synopsis

Abstract

M. Forti and F. Honsell showed in [4] that the hyperuniverses defined in [2] satisfy the anti‐foundation axiom X~1~ introduced in [3]. So it is interesting to study the axiom AFA, which is equivalent to X~1~ in ZF, introduced by P. Aczel in [1]. We show in this paper that AFA is inconsistent with the theory GPK. This theory, which is first order, is defined by E. Weydert in [6] and later by M. Forti and R. Hinnion in [2]. It includes all general hyperuniverses as defined in [5]. In order to achieve our aim, we need to define ordinals in GPK and to study some of their properties.

Mathematics Subject Classification: 03E70, 03E10.