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

摘要

Section 1 is devoted to the study of countable recursively saturated models with an automorphism moving energy non-algebraic point. We show that every countable theory has such a mold 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 in exactly ∪_(n∈N)F~N(φ).