Tom Benhamou

Hill Assistant Professor at
Rutgers University
Department of Mathematics
New Brunswick, NJ

Office Hill 205
E-Mail tom.benhamou at rutgers .edu

Research Interests:

Mathematical Logic and Set Theory: Cardinal arithmetic, singular cardinals, Prikry-type forcings, filters and ultrafilters, infinite combinatorics, set-theoretic topology.
Curriculum Vitae

Our Logic Seminar at Rutgers runs on Monday 3:30 pm Hill 705.

Teaching:

Spring 2024: Math 300: Introduction to Mathematical Reasoning

Spring 2024: Math 461: Mathematical Logic

Past Courses:

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)

Papers and preprints:

Diamond principles and Tukey-top ultrafilters on a countable set, with Fanxin Wu, submitted (2024).

Commutativity of cofinal types ,submitted (2024).

On the Tukey types of Fubini products with Natasha Dobrinen ,submitted (2023).

Transferring Compactness with Jing Zhang ,submitted (2023).

The Galvin Property Under the Ultrapower Axiom with Gabriel Goldberg ,submitted (2023).

Cofinal types of ultrafilters over measurable cardinals with Natasha Dobrinen , JSL (2023).

Small ultrafilter number at every singular cardinal with Sittinon Jirattikansakul ,Acta Mathematica Hungaria (2023) to appear.

Saturation Properties of Ultrafilters in Canonical Inner Models ,submitted (2022).

Non-Galvin Filters,With S. Garti, M. Gitik and A. Poveda ,JML

Galvin's property at large cardinals and partition calculus,With S. Garti and A. Poveda , Israel Journal of Mathematics (2022) to appear.

On Cohen and Prikry forcing notions, With M. Gitik, Journal of symbolic logic (2022) to appear.

Negating the Galvin Property, With S. Garti and A. Poveda, to appear in the Journal of the London Mathematical Society(2021) to apear.

The Variety of Projections of a Tree Prikry Forcing, With M. Gitik and Y. Hayut, Journal of Mathematical Logic (2021) to appear.

Kurepa trees and the failure of the Galvin property, With S. Garti and S. Shelah, Proceedings of the American Mathematical Society, (2022).

Intermediate Models of Magidor-Radin Forcing- Part II, With M. Gitik, Annals of Pure and Applied Logic 173, 103107 (2022).

Intermediate models of Magidor-Radin Forcing. I, With M. Gitik Isr. J. Math, doi.org/10.1007/s11856-022-2335-1. (2022).

Sets in Prikry and Magidor Generic Extensions,With M. Gitik Annals of Pure and Applied Logic 172, 102926 (2021).

Prikry forcing and Tree Prikry Porcing of Various Filters, Arch. Math. Logic vol 58, 787–817(2019) .

Some Slides:

Commutativity of Cofinal types of ultrafilter UC Berkeley Logic Colloquium (2024).

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

Filters and Ultrafilters RUMA (2024).

Cofinal Types of Ultrafilters over Measure and Non-measurable Cardinals VCU (2023).

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).

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