Zachiri McKenzie

activity

20132026

most citedInitial self-embeddings of models of set theory

2 citations · 5 across the 11 of their papers we have counts for

collaborators

15 papers

math.LO2026

On a slight weakening of Kripke-Platek Set Theory

Zachiri McKenzie

The weak set theory $ReR$ is obtained from Kripke-Platek Set Theory ( $KP$ ) by replacing the bounded collection scheme with the bounded replacement scheme. We show…

math.LO2025

The set-theoretic Kaufmann-Clote question

Zachiri McKenzie

Let $M$ be the set theory obtained from $ZF$ by removing the collection scheme, restricting separation to $Δ_{0}$ -formulae and adding an axiom asserting that every…

math.LO2024

Partially-elementary end extensions of countable models of set theory

Zachiri McKenzie

Let $KP$ denote Kripke-Platek Set Theory and let $M$ be the weak set theory obtained from $ZF$ by removing the collection scheme, restricting separation…

math.LO2022

Partially-elementary end extensions of countable admissible sets

Zachiri McKenzie

A result of Kaufmann shows that if $L_{α}$ is countable, admissible and satisfies $Π_{n} -Collection$ , then $⟨ L_{α}, \in ⟩$ has a proper $Σ_{n + 1}$ -elementary end ext…

math.LO2021

End extending models of set theory via power admissible covers

Zachiri McKenzie, Ali Enayat

Motivated by problems involving end extensions of models of set theory, we develop the rudiments of the power admissible cover construction (over ill-founded models of set theory),…

math.LO2020

The subset relation and $2$ -stratified sentences in set theory and class theory

Zachiri McKenzie

Hamkins and Kikuchi (2016 and 2017) show that in both set theory and class theory the definable subset ordering of the universe interprets a complete and decidable theory. If $\mat…

math.LO2019★ 2 cited

Initial self-embeddings of models of set theory

Ali Enayat, Zachiri McKenzie

By a classical theorem of Harvey Friedman (1973), every countable nonstandard model $M$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding $…

math.LO2018

On the relative strengths of fragments of collection

Zachiri McKenzie

Let $M$ be the basic set theory that consists of the axioms of extensionality, emptyset, pair, union, powerset, infinity, transitive containment, $Δ_{0}$ -separation and set…

math.LO2017

Iterated Ultrapowers for the Masses

Ali Enayat, Matt Kaufmann, Zachiri McKenzie

We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indisc…

math.GR2016★ 2 cited

$X$ -torsion and universal groups

Maurice Chiodo, Zachiri McKenzie

For a set $X \subseteq N$ , we define the $X$ -torsion of a group $G$ to be all elements $g \in G$ with $g^{n} = e$ for some $n \in X$ . With $X$ recursively enumerable, we give t…

math.LO2016

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

Ali Enayat, Matt Kaufmann, Zachiri McKenzie

Given a model $M$ of set theory, and a nontrivial automorphism $j$ of $M$ , let $I_{fix} (j)$ be the submodel of $M$ whose universe c…

math.LO2016

Feferman's Forays into the Foundations of Category Theory

Ali Enayat, Paul Gorbow, Zachiri McKenzie

This paper is primarily concerned with assessing a set-theoretical system, $S^{*}$ , for the foundations of category theory suggested by Solomon Feferman. $S^{*}$ is an extension of NFU…

math.LO2016

On the strength of a weak variant of the Axiom of Counting

Zachiri McKenzie

In this paper $NFU^{- AC}$ is used to denote Ronald Jensen's modification of Quine's `New Foundations' Set Theory ( $NF$ ) fortified with a type-level pairi…

math.LO2014★ 1 cited

Decidable fragments of the Simple Theory of Types with Infinity and NF

Anuj Dawar, Thomas Forster, Zachiri McKenzie

We identify complete fragments of the Simple Theory of Types with Infinity ( $TSTI$ ) and Quine's $NF$ set theory. We show that $TSTI$ decides every senten…

math.LO2013

Automorphisms of models of set theory and extensions of NFU

Zachiri McKenzie

In this paper we exploit the structural properties of standard and non-standard models of set theory to produce models of set theory admitting automorphisms that are well-behaved a…

On a slight weakening of Kripke-Platek Set Theory

The set-theoretic Kaufmann-Clote question

Partially-elementary end extensions of countable models of set theory

Partially-elementary end extensions of countable admissible sets

End extending models of set theory via power admissible covers

The subset relation and 2-stratified sentences in set theory and class theory

Initial self-embeddings of models of set theory

On the relative strengths of fragments of collection

Iterated Ultrapowers for the Masses

X-torsion and universal groups

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

Feferman's Forays into the Foundations of Category Theory

On the strength of a weak variant of the Axiom of Counting

Decidable fragments of the Simple Theory of Types with Infinity and NF

Automorphisms of models of set theory and extensions of NFU

The subset relation and $2$ -stratified sentences in set theory and class theory

$X$ -torsion and universal groups