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

Journal of Symbolic Logic 63 (3):815-830 (1998)
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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 $\bigcup_{n\in \mathbb{N}}\mathscr{P}^n(\varnothing)$



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Iterated ultrapowers for the masses.Ali Enayat, Matt Kaufmann & Zachiri McKenzie - 2018 - Archive for Mathematical Logic 57 (5-6):557-576.
Automorphisms of models of arithmetic: a unified view.Ali Enayat - 2007 - Annals of Pure and Applied Logic 145 (1):16-36.
Transplendent Models: Expansions Omitting a Type.Fredrik Engström & Richard W. Kaye - 2012 - Notre Dame Journal of Formal Logic 53 (3):413-428.
Automorphisms with only infinite orbits on non-algebraic elements.Grégory Duby - 2003 - Archive for Mathematical Logic 42 (5):435-447.

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Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Logic for Mathematicians.H. B. Enderton - 1980 - Journal of Symbolic Logic 45 (3):631-632.

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