# Automorphisms of models of set theory and extensions of NFU

@article{McKenzie2015AutomorphismsOM,
title={Automorphisms of models of set theory and extensions of NFU},
author={Zachiri McKenzie},
journal={Ann. Pure Appl. Log.},
year={2015},
volume={166},
pages={601-638}
}
• Zachiri McKenzie
• Published 18 September 2013
• Materials Science
• Ann. Pure Appl. Log.
7 Citations

### INITIAL SELF-EMBEDDINGS OF MODELS OF SET THEORY

• Mathematics
The Journal of Symbolic Logic
• 2021
Abstract By a classical theorem of Harvey Friedman (1973), every countable nonstandard model $\mathcal {M}$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding j, i.e.,

### Largest initial segments pointwise fixed by automorphisms of models of set theory

• Mathematics
Arch. Math. Log.
• 2018

### ALGEBRAIC NEW FOUNDATIONS

A novel categorical set theory, MLCat, is proved to be equiconsistent to New Foundations (NF), and which can be modulated to correspond to intuitionistic or classical NF, with atoms.

### Largest initial segments pointwise fixed by automorphisms of models of set theory

• Materials Science
Archive for Mathematical Logic
• 2017
Given a model M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}

## References

SHOWING 1-10 OF 28 REFERENCES

### Automorphisms , Mahlo Cardinals , and NFU

In this paper we establish an intimate relationship between Mahlo cardinals and automorphisms of models of set theory. The models of set theory involved here are not well-founded since a routine

### On the Consistency of a Slight (?) Modification of Quine’s New Foundations

Quine’s system of set theory, New Foundations (NF), can be conveniently formalized as a first-order theory containing two predicates ≡ (identity) and e (set membership). One of the most attractive

### Strong axioms of infinity in NFU

This paper discusses a sequence of extensions of NFU, Jensen's improvement of Quine's set theory “New Foundations” (NF) of [16], which was to restrict extensionality to sets, allowing many non-sets (urelements) with no elements.

### Finite Sets in Quine's New Foundations

Some axiomatic systems of set theory related to the system NF (New Foundations) of Quine are considered, including the possible relations of cardinality between a finite set x and its subset class SC(x) = { y | y ∩ x} and also between X and its unit set class USC(x).

### FROM BOUNDED ARITHMETIC TO SECOND ORDER ARITHMETIC VIA AUTOMORPHISMS

In this paper we examine the relationship between automorphisms of models of I∆0 (bounded arithmetic) and strong systems of arithmetic, such as PA, ACA0 (arithmetical comprehension schema with

### Permutations and wellfoundedness: the true meaning of the bizarre arithmetic of Quine's NF

• T. Forster
• Mathematics, Philosophy
Journal of Symbolic Logic
• 2006
It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings.

### End-extensions preserving power set

• Mathematics
Journal of Symbolic Logic
• 1991
Abstract We consider the quantifier hierarchy of Takahashi [1972] and show how it gives rise to reflection theorems for some large cardinals in ZF, a new natural subtheory of Zermelo's set theory, a

### The consistency strength of NFUB

We show that the consistency strength of the system NFUB, a variant of Quine's "New Foundations" recently introduced by Randall Holmes, is precisely that of [ZFC - Power Set] + "There is a weakly