## Journal of Symbolic Logic

### Automorphisms Moving all Non-Algebraic Points and an Application to NF

Friederike Korner

#### Abstract

Section 1 is devoted to the study of countable recursively saturated models with an automorphism moving every non-algebraic point. We show that every countable theory has such a model and exhibit necessary and sufficient conditions for the existence of automorphisms moving all non-algebraic points. Furthermore we show that there are many complete theories with the property that every countable recursively saturated model has such an automorphism. In Section 2 we apply our main theorem from Section 1 to models of Quine's set theory New Foundations (NF) to answer an old consistency question. If NF is consistent, then it has a model in which the standard natural numbers are a definable subclass $\mathbb{N}$ of the model's set of internal natural numbers Nn. In addition, in this model the class of wellfounded sets is exactly $\bigcup_{n\in \mathbb{N}}\mathscr{P}^n(\varnothing)$.

#### Article information

Source
J. Symbolic Logic, Volume 63, Issue 3 (1998), 815-830.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745568

Mathematical Reviews number (MathSciNet)
MR1649063

Zentralblatt MATH identifier
0919.03031

JSTOR