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Automorphisms moving all non-algebraic points and an application to NF

Published online by Cambridge University Press:  12 March 2014

Friederike Körner
Friederike Körner*
Affiliation:
Technische Universität Berlin, FB 3 (Mathematik), Strasse des 17. Juni 136. D – 10623 Berlin, Germany E-mail: [email protected]
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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 ℕ of the model's set of internal natural numbers Nn. In addition, in this model the class of wellfounded sets is exactly .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 815 - 830
Copyright
Copyright © Association for Symbolic Logic 1998

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