Models of Self-Descriptive Set Theories
Marco Forti, Furio Honsell · Birkhäuser Boston eBooks · 1989
It is well known that Zermelo-Fraenkel set theory has a limited self-descriptive power. In fact most of the basic set-theoretic relations, operations and properties (e.g. membership, union, sethood) cannot be represented as sets since the classes which correspond to them are too large. Many attempts have been made to define set theories consistent relative to ZF, which allow as sets many interesting classes having the size of the universe. Apart from W.V.O.Quine’s NF [16], whose consistency strength is still unknown, we can mention the theories (all equiconsistent with ZF) considered by A.Church [1], H.Friedman [11], E.Mitchell [14], and A.Oberschelp [15]. These, however, are in some sense unsatisfactory, since each of them is not closed under some basic construction. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.