Set theory & mathematical logic

Tom Benhamou

Senior Lecturer (Assistant Professor)
School of Mathematical Sciences · Tel Aviv University

Faculty profile · Curriculum vitae

tombenhamou@tauex.tau.ac.il

Research

• Mathematical Logic and Set Theory: Cardinal arithmetic, singular cardinals, Prikry-type forcings, filters and ultrafilters, infinite combinatorics, set-theoretic topology.
• Curriculum Vitae
  
  TAU Set Theory Seminar, organized by Tom Benhamou.
  Previously: Rutgers Logic Seminar.

Past courses

• Spring 2024: Math 461: Mathematical Logic

• Fall 2025: Math 251: Calculus III

• Fall 2025: Math 151: Calculus I

• Spring 2025: Math 300: Introduction to Mathematical Reasoning

• Fall 2024: Math 300: Introduction to Mathematical Reasoning

• Fall 2024: Math 250: Introductory Linear Algebra

• Spring 2024: Math 300: Introduction to Mathematical Reasoning

• Spring 2024: Math 461: Mathematical Logic

• Fall 2023: Math 361: Set Theory

• Spring 2022(UIC): Math 504: Set Theory

• Fall 2022(UIC): Math 215: Introduction to advanced mathematics I

• Introduction to Set Theory (2017-2022) (Tel-Aviv University)

• Linear Algebra(Tel-Aviv University)

Publications

Preprints

1. Stationary Limits of the Point Spectrum. with H. Jakob. 2026.
   Author’s copy
2. Compactness phenomena in HOD and the Optimality of Magidor’s Covering theorem. with J. Cummings, G. Goldberg, Y. Hayut, and A. Poveda. 2026.
   Author’s copy
3. On the intermediate models of the Strongly compact Prikry forcing. with S. Thei and B. Weltsch. 2026.
   Author’s copy
4. Scales in the Point Spectrum. 2026.
   Author’s copy
5. On the asymptotic behavior of guessing sequences. with Sean Leclair. 2026.
   Author’s copy
6. Forms of Rapidness and powers of ideals. 2026.
   Author’s copy
7. Commutativity of cofinal types (earlier version). 2026.
   Author’s copy
8. Eventual Capturing on a measurable. with C. Switzer. 2025.
   Author’s copy
9. Tukey idempotency and strong p-points. with N. Dobrinen and T. Özalp. 2025.
   Author’s copy
10. Isomorphism classes of generating sets. with J. Cummings, G. Goldberg, Y. Hayut, and A. Poveda. 2025.
    Author’s copy
11. On Ultrapowers and Cohesive Ultrafilters. 2024.
    Author’s copy
12. Non-normal Magidor-Radin types of forcings. with A. Poveda. 2024.
    Author’s copy

Published & accepted

1. Supercompact Measures and the Galvin Property. with B. Weltsch. Journal of Symbolic Logic, to appear (2026).
   Author’s copy Journal
2. Applications of the Magidor iteration to Ultrafilter Theory. with G. Goldberg. Forum of Mathematics, Sigma 14: e61 (2026).
   Author’s copy Journal
3. Stationary Reflection and the Failure of SCH at ℵ_ω₁. with D. Sinapova. Transactions of the American Mathematical Society, to appear (2024).
   Author’s copy Journal
4. Ultrafilters over uncountable cardinals and the Tukey order. with J. T. Moore and L. Serafin. Fundamenta Mathematicae 272: 271–305 (2026).
   Author’s copy Journal
5. Cardinals of the P_κ(λ)-filter games. with V. Gitman. Israel Journal of Mathematics, to appear (2026).
   Author’s copy
6. Diamond principles and Tukey-top ultrafilters on a countable set. with F. Wu. Topology and its Applications 381: 109739 (2026).
   Author’s copy Journal
7. Measures that violate the generalized continuum hypothesis. with G. Goldberg. Advances in Mathematics 487: 110778 (2026).
   Author’s copy Journal
8. Saturation Properties in Canonical Inner Models. Journal of Mathematical Logic, to appear (2025).
   Author’s copy Journal
9. On the Tukey types of Fubini products. with N. Dobrinen. Proceedings of the American Mathematical Society, Series B, 12: 103–117 (2025).
   Author’s copy Journal
10. The Galvin property under the Ultrapower Axiom. with G. Goldberg. Canadian Journal of Mathematics 77(5): 1686–1717 (2025).
    Author’s copy Journal
11. Cofinal types of ultrafilters over measurable cardinals. with N. Dobrinen. The Journal of Symbolic Logic 90(4): 1801–1835 (2025).
    Author’s copy Journal
12. Non-Galvin filters. with S. Garti, M. Gitik, and A. Poveda. Journal of Mathematical Logic 25(02): 2450017 (2025).
    Author’s copy Journal
13. Galvin’s property at large cardinals and an application to partition calculus. with S. Garti and A. Poveda. Israel Journal of Mathematics 269: 143–184 (2025).
    Author’s copy Journal
14. Transferring Compactness. with J. Zhang. Journal of the London Mathematical Society 109(6): e12940 (2024).
    Author’s copy Journal
15. The variety of projections of a tree-Prikry forcing. with M. Gitik and Y. Hayut. Journal of Mathematical Logic 24(03): 2450006 (2024).
    Author’s copy Journal
16. Kurepa trees and the failure of the Galvin property. with S. Garti and S. Shelah. Proceedings of the American Mathematical Society 151: 1301–1309 (2023).
    Author’s copy Journal
17. On Cohen and Prikry forcing notions. with M. Gitik. The Journal of Symbolic Logic 89(2): 858–904 (2023).
    Author’s copy Journal
18. Negating the Galvin property. with S. Garti and A. Poveda. Journal of the London Mathematical Society 108(1): 190–237 (2023).
    Author’s copy Journal
19. Small ultrafilter number at every singular cardinal. with S. Jirattikansakul. Acta Mathematica Hungaria 171: 12–38 (2023).
    Author’s copy Journal
20. Intermediate models of Magidor-Radin forcing — Part II. with M. Gitik. Annals of Pure and Applied Logic 173(6): 103107 (2022).
    Author’s copy Journal
21. Intermediate models of Magidor-Radin forcing — Part I. with M. Gitik. Israel Journal of Mathematics 252: 47–94 (2022).
    Author’s copy Journal
22. Sets in Prikry and Magidor generic extensions. with M. Gitik. Annals of Pure and Applied Logic 172(4): 102926 (2021).
    Author’s copy Journal
23. Prikry forcing and tree Prikry forcing of various filters. Archive for Mathematical Logic 58: 787–817 (2019).
    Author’s copy Journal

Slides and seminar notes

• The PCF Theory of Directed Sets
  European Set Theory Conference, Helsinki, Finland (2026).
• On the Structure of an Ultrafilter Basis
  Slides.
• The Cofinality of Ultrafilters
  University of North Texas (2026).
• On the Intermediate Models of Strongly Compact Prikry Forcing
  TAU Set Theory Seminar series — seminar notes (2026).

Earlier slides

• Tukey-top ultrafilters under UA CUNY Set theory seminar (2024).

• Filters and Ultrafilters RUMA (2024).

• The Galvin Property Under UA HUJI Set Theory Seminar (2023).

• Galvin's Property at Large Cardinals JMM Boston (2023).

• Intermediate Models of Prikry-Type Forcings Rutgers Logic Seminar (2022).

• The Galvin Property at Successors of Singular Cardinals Advances in Set Theory- Jerusalem (2022).

• The Forcing Method and Prikry-type Forcings IMU (2020).