Pseudo-Superstructures as Nonstandard Universes

A definition of nonstandard universe which gets over the limitation to the finite levels of the cumulative hierarchy is proposed. Though necessarily nonwellfounded, nonstandard universes are arranged in strata in the likeness of superstructures and allow a rank function taking linearly ordered values. Nonstandard universes are also constructed which model the whole ZFC theory without regularity and satisfy the κ-saturation property.

• Type: Journal
• Year: 1998
• Where: JSYML
• Authors: Mauro Di Nasso
• Keywords: Cumulative Hierarchy, JSYML 1998, Nonstandard Universes, finite Levels