## 7 Citations

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

- MathematicsThe 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

- MathematicsArch. Math. Log.
- 2018

The main achievement is the calculation of the theory of the Theory of C of structures of the form C as precisely MOST-Δ0P-MOST, a recursively saturated model of MOST that is closed under exponentiation and contains $\omega ^\mathcal {M}$$ωM.

### Self-similarity in the Foundations

- MathematicsThe Bulletin of Symbolic Logic
- 2019

This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory, and the formulation of a novel algebraic set theory which is proved to be equiconsistent to New Foundations, and which can be modulated to correspond to intuitionistic or classical NF.

### On the strength of a weak variant of the axiom of counting

- Materials ScienceMath. Log. Q.
- 2017

It is shown that Ronald Jensen's modification of Quine's `New Foundations' Set Theory ($\mathrm{NF}$) fortified with a type-level pairing function but without the Axiom of Choice proves the consistency of the Simple Theory of Types with Infinity.

### On the relative strengths of fragments of collection

- MathematicsMath. Log. Q.
- 2019

This paper studies the relative strength of set theories obtained by adding fragments of the set-theoretic collection scheme to $\mathbf{M}$ and proves the consistency of Zermelo Set Theory plus strong $\Pi_n$-collection.

### ALGEBRAIC NEW FOUNDATIONS

- MathematicsThe Journal of Symbolic Logic
- 2019

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 ScienceArchive 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

- Mathematics
- 2004

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

- Mathematics
- 1968

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

- PhilosophyJournal of Symbolic Logic
- 2001

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

- MathematicsJ. Symb. Log.
- 1969

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

- Mathematics
- 2005

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

- Mathematics, PhilosophyJournal 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

- MathematicsJournal 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

- Computer Science
- 1997

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…