par Esser, Olivier
Référence Mathematical logic quarterly, 42, 1, page (104-108)
Publication Publié, 1996
Article révisé par les pairs
Résumé : M. Forti and F. Honsell showed in [4] that the hyperuniverses denned in [2] satisfy the anti-foundation axiom X1 introduced in [3]. So it is interesting to study the axiom AFA, which is equivalent to X1 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 denned 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.