Maxwell Levine

About Me

Papers

• "Failure of Approachability at the Successor of the First Singular for any Cofinality" (with Hannes Jakob), submitted. [pdf]
• "Good Scales and Non-Compactness of Squares (with Heike Mildenberger), submitted (revised in May 2025). [pdf]
• "On Namba Forcing and Minimal Collapses", submitted (revised in June 2025). [pdf]
• "Distinguishing Internally Club and Approachable on an Infinite Interval" (with Hannes Jakob), Bulletin of the London Mathematical Society, 57(4):1026-1039, 2025. [pdf/link]
• "Classical Namba Forcing Can Have the Weak Countable Approximation Property", to appear in Proceedings of the American Mathematical Society. [pdf]
• "On Disjoint Stationary Sequences", Pacific Journal of Mathematics, 332(1):147-165, 2024. [pdf/link]
• "Unthreadability with Small Conditions", submitted (under revision with a tentative update in the link). [pdf]
• "On Compactness of Weak Square at Singulars of Uncountable Cofinality", to appear in Journal of Symbolic Logic. [pdf/link]
• "Distributivity and Minimality in Perfect Tree Forcings for Singular Cardinals" (with Heike Mildenberger), Israel Journal of Mathematics, 261(2):541-588, 2024. [pdf/link]
• "Trees and Stationary Reflection at Double Successors of Regular Cardinals" (with Thomas Gilton and Šárka Stejskalová), Journal of Symbolic Logic, 88(2): 780-810, 2023. [arxiv/link]
• "Patterns of Stationary Reflection" (with Sy-David Friedman), Israel Journal of Mathematics, 249(1):1-35, 2022. [pdf/link]
• "Squares and Uncountably Singularized Cardinals" (with Dima Sinapova), Fundamenta Mathematicae, 253(3):277-296, 2021. [pdf/link]
• "Partitioning a Reflecting Stationary Set" (with Assaf Rinot), Proceedings of the American Mathematical Society, 148(8):3551-3565, 2020. [pdf/link]
• "The Semi-Weak Square Principle", Annals of Pure and Applied Logic, 170(11):102713, 2019. [pdf/link]
• "Stationary Sets Added When Forcing Squares", Archive for Mathematical Logic, 57(7):909-916, 2018. [pdf/link]
• "Weak Squares and Very Good Scales", Journal of Symbolic Logic, 83(1):1-12, 2018. [link]

Teaching

• For the Summer 2025 Semester, I am managing a seminar on the axiom of choice with Heike Mildenberger.
• At the University of Freiburg, I have taught short courses in Large Cardinals in Set Theory (notes), Models of Peano Arithmetic, and Descriptive Set Theory (notes), Applications of Set Theory (notes), and an Introduction to Set Theory and Independence proofs (website). I have also tutored student seminars in Ramsey Theory, Knot Theory, Cryptography, Representation Theory, Algebraic Topology, and Differential Topology.
• At the University of Freiburg, I am mentoring Simon Klemm for his master's thesis on the proper forcing axiom.
• At the University of Illinois at Chicago, I taught a number of courses including: Intermediate Algebra, Calculus I, Calculus II, Calculus III, Calculus for Business, and Elementary Linear Algebra.

Contact Information

• postal:
  Albert-Ludwigs-Universität Freiburg
  Mathematisches Institut
  Ernst-Zermelo-Straße 1
  79104 Freiburg im Breisgau
  Germany
• email: maxwell(dot)levine(at)mathematik(dot)uni-freiburg(dot)de
• office: 311

© 2015-present Maxwell Levine