About

Justin Moore is a professor in the Department of Mathematics at Cornell University, located in Malott Hall. He earned his Ph.D. from the University of Toronto in 2000. His primary research interests include set theory, infinite combinatorics, and their applications to other fields of mathematics such as topology, functional analysis, and algebra. Recently, his work has focused on improving the understanding of groups closely related to the group of piecewise linear homeomorphisms of the unit interval.

Research topics

• Mathematics
• Combinatorics
• Discrete mathematics
• Pure mathematics
• Computer science

Selected publications

• Ultrafilters over uncountable cardinals and the Tukey order

  Fundamenta Mathematicae · 2026-03-20

  articleOpen access

  We study ultrafilters on regular uncountable cardinals, with a primary focus on ω1, and particularly in relation to the Tukey order on directed sets. Results include the independence from ZFC of the assertion that every uniform ultrafilter over ω1 is Tukey-equivalent to [2ℵ1]<ω, and for each cardinal κ of uncountable cofinality, a new construction of a uniform ultrafilter over κ which extends the club filter and is Tukey-equivalent to [2κ]<ω. We also analyze Todorcevic’s ultrafilter U(T) under PFA, proving that it is Tukey-equivalent to [2ℵ1]<ω and that it is minimal in the Rudin–Keisler order with respect to being a uniform ultrafilter over ω1. We prove that, unlike PFA, MAω1 is consistent with the existence of a coherent Aronszajn tree T for which U(T) extends the club filter. A number of other results are obtained concerning the Tukey order on uniform ultrafilters and on uncountable

  PublisherOA PDFDOI

• The method of forcing

  Topology and its Applications · 2025-07-04 · 1 citations

  preprintOpen access1st authorCorresponding
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• A virtual five element basis for the uncountable linear orders

  ArXiv.org · 2025-10-04

  preprintOpen accessSenior author

  We prove that for every Aronzsajn line A and every Countryman line C, there is a proper forcing extension in which A contains an isomorphic copy of either C or its converse C*. As a corollary, we obtain answers to several related questions asked by the second author in the literature: if there is an inaccessible cardinal, then there is a proper forcing extension in which the uncountable linear orders have a five element basis; BPFA implies the existence of a five element basis for the uncountable linear orders; BPFA is equiconsistent with the conjunction of BPFA and Aronszajn tree saturation. These results are derived from new preservation results concerning subtrees of Aronszajn trees, proper forcings, and countable support iterations, generalizing work of Miyamoto, Abraham, and Shelah.

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• A piecewise linear homeomorphism of the circle preserving rational points and periodic under renormalization

  Groups Geometry and Dynamics · 2025-12-08

  articleOpen accessSenior author

  We demonstrate the existence of a piecewise linear homeomorphism f of \mathbb{R}/\mathbb{Z} which maps rationals to rationals, whose slopes are powers of \frac{2}{3} and whose rotation number is \sqrt{2}-1 . This is achieved by showing that a renormalization procedure becomes periodic when applied to f . Our construction gives a negative answer to a question of D. Calegari (2007). When combined with the results by J. Hyde and J. Tatch Moore (2023), our result also shows that F_{\frac{2}{3}} does not embed into F , where F_{\frac{2}{3}} is the subgroup of the Stein–Thompson group F_{2,3} consisting of those elements whose slopes are powers of \frac{2}{3} . Finally, we produce some evidence suggesting a positive answer to a variation of Calegari’s question and record a number of computational observations.

  PublisherDOI

• A descriptive approach to higher derived limits

  Journal of the European Mathematical Society · 2024-06-06 · 3 citations

  articleOpen access

  We present a new aspect of the study of higher derived limits. More precisely, we introduce a complexity measure for the elements of higher derived limits over the directed set \Omega of functions from \mathbb{N} to \mathbb{N} and prove that cocycles of this complexity are images of cochains of roughly the same complexity. In the course of this work, we isolate a partition principle for powers of directed sets and show that whenever this principle holds, the corresponding derived limit \lim\nolimits^{n} is additive; vanishing results for this limit are the typical corollary. The formulation of this partition hypothesis synthesizes and clarifies several recent advances in this area.

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• On minimal non-σ-scattered linear orders

  Advances in Mathematics · 2024-02-21 · 1 citations

  articleSenior authorCorresponding
  PublisherDOI

• Subgroups of $\mathrm{PL}_{+} I$ which do not embed into Thompson’s group $F$

  Groups Geometry and Dynamics · 2023-03-17 · 2 citations

  articleOpen accessSenior author

  We will give a general criterion—the existence of an F - obstruction —for showing that a subgroup of \mathrm{PL}_{+} I does not embed into Thompson’s group F . An immediate consequence is that Cleary’s “golden ratio” group F_\tau does not embed into F , answering a question of Burillo, Nucinkis, and Reves. Our results also yield a new proof that Stein’s groups F_{p,q} do not embed into F , a result first established by Lodha using his theory of coherent actions. We develop the basic theory of F -obstructions and show that they exhibit certain rigidity phenomena of independent interest. In the course of establishing the main result of the paper, we prove a dichotomy theorem for subgroups of \mathrm{PL}_{+} I . In addition to playing a central role in our proof, it is strong enough to imply both Rubin’s reconstruction theorem restricted to the class of subgroups of \mathrm{PL}_{+} I and also Brin’s ubiquity theorem.

  PublisherDOI

• On minimal non-$σ$-scattered linear orders

  arXiv (Cornell University) · 2023-04-06

  preprintOpen accessSenior author

  The purpose of this article is to give new constructions of linear orders which are minimal with respect to being non-$σ$-scattered. Specifically, we will show that Jensen's principle $\diamondsuit$ implies that there is a minimal Countryman line, answering a question of Baumgartner. We also produce the first consistent examples of minimal non-$σ$-scattered linear orders of cardinality greater than $\aleph_1$, as given a successor cardinal $κ^+$, we obtain such linear orderings of cardinality $κ^+$ with the additional property that their square is the union of $κ$-many chains. We give two constructions: directly building such examples using forcing, and also deriving their existence from combinatorial principles. The latter approach shows that such minimal non-$σ$-scattered linear orders of cardinality $κ^+$ exist for every cardinal $κ$ in Gödel's constructible universe, and also (using work of Rinot) that examples must exist at successors of singular strong limit cardinals in the absence of inner models satisfying the existence of a measurable cardinal $μ$ of Mitchell order $μ^{++}$.

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• A descriptive approach to higher derived limits

  arXiv (Cornell University) · 2022-03-01

  preprintOpen access

  We present a new aspect of the study of higher derived limits. More precisely, we introduce a complexity measure for the elements of higher derived limits over the directed set $Ω$ of functions from $\mathbb{N}$ to $\mathbb{N}$ and prove that cocycles of this complexity are images of cochains of the roughly the same complexity. In the course of this work, we isolate a partition principle for powers of directed sets and show that whenever this principle holds, the corresponding derived limit $\mathrm{lim}^n$ is additive; vanishing results for this limit are the typical corollary. The formulation of this partition hypothesis synthesizes and clarifies several recent advances in this area.

  PublisherOA PDFDOI

• A piecewise linear homeomorphism of the circle which is periodic under renormalization

  2022-11-10

  preprintOpen accessSenior author

  We demonstrate the existence of a piecewise linear homeomorphism $f$ of $\mathbb{R}/\mathbb{Z}$ which maps rationals to rationals, whose slopes are powers of $\frac{2}{3}$, and whose rotation number is $\sqrt{2}-1$. This is achieved by showing that a renormalization procedure becomes periodic when applied to $f$. Our construction gives a negative answer to a question of D. Calegari. When combined with work of the 2nd and 3rd authors, our result also shows that $F_{\frac{2}{3}}$ does not embed into $F$, where $F_{\frac{2}{3}}$ is the subgroup of the Stein-Thompson group $F_{2,3}$ consisting of those elements whose slopes are powers of $\frac{2}{3}$. Finally, we produce some evidence suggesting a positive answer to a variation of Calegari's question and record a number of computational observations.

  PublisherOA PDFDOI

Frequent coauthors

• Rogier W. Sanders

  Cornell University

  355 shared

• Per Johan Klasse

  Cornell University

  178 shared

• Andrew B. Ward

  Scripps Research Institute

  151 shared

• Thomas J. Ketas

  Cornell University

  147 shared

• Ian A. Wilson

  Scripps Research Institute

  130 shared

• David D. Ho

  Columbia University

  129 shared

• James Μ. Binley

  San Diego Biomedical Research Institute

  113 shared

• Dennis R. Burton

  Scripps Research Institute

  109 shared

Education

• PhD, Mathematics

  University of Toronto

  2000

• MA, Mathematics

  Miami University

  1996

• BS, Mathematics, Physics - double major

  Miami University

  1996