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

Journal of Symbolic Logic 63 (3):815-830 (1998)

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 $\bigcup_{n\in \mathbb{N}}\mathscr{P}^n(\varnothing)$
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2586714
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 40,000
Through your library

References found in this work BETA

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

Add more references

Citations of this work BETA

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.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
17 ( #462,675 of 2,236,147 )

Recent downloads (6 months)
4 ( #460,511 of 2,236,147 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature