LAB LOGA page on LabLog, a review site (not the lab's official page)
Usuba Lab
Machine-translated · View original
The lab studies set theory, which underpins the foundations of mathematics, including large cardinals and the axiom of choice.
AboutAbout the lab
Exploring the foundations of mathematics through set theory.
The Usuba Lab studies axiomatic set theory, a foundational field of mathematics.
In particular, it studies set theory related to "large cardinals," which measure the size of sets, and the "axiom of choice," one of the axioms underlying mathematics.
As an application, the lab also works on set-theoretic topology, which uses set theory to investigate the properties of spaces.
Key terms
- Large cardinal
- A mathematical concept concerning the size of sets that is larger than ordinary infinities
- Axiom of choice
- One of the axioms (assumptions) underlying mathematics, a rule about how elements can be chosen from sets
- Topology
- A field that mathematically studies the "closeness" and connectedness of figures and spaces
ResearchResearch themes
The Usuba Lab studies axiomatic set theory, especially set theory related to large cardinals and the axiom of choice. As an application, it also works on areas such as set-theoretic topology.
*Illustrative imageSet Theory Without the Axiom of Choice
How much can be proved without assuming the axiom of choice, one of the axioms underlying mathematics? The lab investigates the behavior of ultraproducts and large cardinals in a world without the axiom of choice, clarifying how the foundations of mathematics work.
*Illustrative imageNumbers Measuring Infinite Size
Using methods of set theory, the lab studies how numbers related to the "size" of the infinite world behave, such as the number of ultrafilters on an infinite set and the chromatic numbers of graphs of uncountable size.
MembersFaculty
The members of the Usuba Lab consist of faculty members.
- ProfessorToshimichi Usuba
VoicesStudent voices
Compiled from answers by students who were in the lab. Ratings and reviews reflect individual students' experiences, not the lab's official views.
Students who take part in an interview may receive a thank-you gift worth ¥1,000, regardless of what they say.
On a 4-point scale, ● marks where students' answers fall
Who is this lab for?
What's great about this lab?
What did you learn after joining?
What's the vibe, and what is the professor like?
Where do graduates go?
RelatedLabs similar to Usuba Lab
Yoneda LabSchool of Fundamental Science and Engineering, Department of MathematicsMathematics of relativity
Ikeda LabSchool of Fundamental Science and Engineering, Department of MathematicsGeometry, representation theory, combinatorics
Ogawa LabSchool of Fundamental Science and Engineering, Department of MathematicsTheory of partial differential equations, real analysis, fun…
Ozaki LabSchool of Fundamental Science and Engineering, Department of MathematicsAlgebraic number theoryThe information on this page is compiled by the LabLog team from the lab's public information and interviews. For corrections or removal requests, please contact LabLog, not the lab.
Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique” Jérémy Barande / CC BY-SA 3.0 (cropped)
- Set Theory Without the Axiom of Choice: “Georg Cantor (Porträt)” 作者不詳 / Public domain (cropped)
- Numbers Measuring Infinite Size: “Hilbert's Hotel” Jan Beránek / CC BY-SA 4.0 (cropped)
- Related lab (米田研究室): “Maya-NR-Simulation-with-Waveform-frame788” Deborah Ferguson ほか、
Georgia Tech MAYA Collaboration / CC BY-SA 4.0 (cropped) - Related lab (池田研究室): “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
- Related lab (小川研究室): “Chladni plate 14” Exhibit made by Estes Objethos Atelier, photo by Rodrigo Tetsuo Argenton / CC BY-SA 4.0 (cropped)
- Related lab (尾﨑研究室): “Minoritenkirche rose window - Vienna” MrPanyGoff / CC BY-SA 3.0 (cropped)
About LabLog
LabLog is a lab review app for students only. Student members at each university interview students in labs and publish what they say. Student voices can only be read by students who sign up with a university email address. Operated by bestiee Inc.
Learn more about LabLog ↗Search engines and AI may reference the basic lab info and rating summaries on this page and the description of LabLog. Student voices are for student members only. Automated collection by programs (scraping, or input to or training of AI) is prohibited under Article 8 of the Terms of Service. If you need data for research or analysis, please contact us.