## Journal of Symbolic Logic

### Pseudo-Superstructures as Nonstandard Universes

Mauro Di Nasso

#### Abstract

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 $\kappa$-saturation property.

#### Article information

Source
J. Symbolic Logic, Volume 63, Issue 1 (1998), 222-236.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745467

Mathematical Reviews number (MathSciNet)
MR1610407

Zentralblatt MATH identifier
0902.03040

JSTOR