Set Theory with a Universal Set: Exploring an Untyped Universe
Thomas Förster · 1992
Part 1 Introduction: annotated definitions some motivations and axioms a brief survey how do theories with V E V avoid paradoxes? chronology. Part 2 NF and related systems: NF cardinal and ordinal arithmetic the Kay-Specker equiconsistency lemma remarks on subsystems, term models and prefix classes the converse consistency problem. Part 3 Permutation models: permutation in NF applications to other theories. Part 4 Interpretations in well-founded sets: Church's universal set theory CUS Mitchell's set theory beyond Church, Sheridan and Mitchell. Part 5 Open problems: permutation models and quantifier hierarchies cardinals and ordinals in NF KF Z other subsystems automorphisms and well-founded extensional relations term models miscellaneous.