Dr Zachiri McKenzie

Zach teaches a variety of mathematics courses in both the undergraduate and taught postgraduate mathematics programmes.

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Zach's research investigates the structure of models of set theory, and compares the strength and scope of foundational theories using model-theoretic techniques. In addition to extensions and sub-systems of Zermelo-Fraenkel Set Theory, he is also interested in first and second order arithmetic and their subsystems, the Simple Theory of Types and variants of Quine’s New Foundations Set Theory.

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"The subset relation and 2-stratified sentences in set theory and class theory", to appear in Mathematical Logic Quarterly. 

"End extending models of set theory via power admissible covers" (with Ali Enayat), Annals of Pure and Applied Logic, Volume 173, Issue 8. 2022. 

"Initial self-embeddings of models of set theory" (with Ali Enayat), Journal of Symbolic Logic, Volume 86, Issue 4. 2021. Pages 1584-1611.

"On the relative strengths of fragments of collection", Mathematical Logic Quarterly, Volume 65, Issue 1. 2019. 

"Largest initial segments pointwise fixed by automorphisms of models of set theory" (with Ali Enayat and Matt Kaufmann), Archive for Mathematical Logic, Volume 57, Issues 1-2. 2018. Pages 91-139.

"Iterated ultrapowers for the masses" (with Ali Enayat and Matt Kaufmann), Archive for Mathematical Logic. Volume 57. Issues 5-6. 2018. Pages 557-576. 

"On the strength of a weak variant of the Axiom of Counting", Mathematical Logic Quarterly, Volume 63, Number 1-2. 2017. Pages 94-103.

"Feferman's Forays into the Foundations of Category Theory" (with Ali Enayat and Paul Gorbow), Feferman on Foundations - Logic, Mathematics, Philosophy. Edited by Gerhard Jaeger and Wilfried Sieg. Outstanding Contributions to Logic Series, Volume 13, Springer. 2017. Pages 315-346.

"Decidable fragments of the Simple Theory of Types with Infinity and NF" (with Anuj Dawar and Thomas Forster), Notre Dame Journal of Formal Logic, Volume 58, Number 3. 2017. Pages 433-451.

"Automorphisms of models of set theory and extensions of NFU", Annals of Pure and Applied Logic, Volume 166. 2015. Pages 601-638. 

"A permutation method yielding models of the stratified axioms of Zermelo Fraenkel set theory" (with Vu Dang) appearing in M. Crabbe and T. E. Forster (eds.) Proceedings of the 70th anniversary NF meeting in Cambridge. Cahiers du Centre de Logique, Volume 16, Academia-Bruylant, Louvain-la-Neuve (Belgium). 2009. Pages 9-32.