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Yoshinobu Lab
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A set theory lab that explores the sizes of infinity from axioms.
AboutAbout the lab
Exploring infinite combinatorics through large cardinal axioms.
Professor Yoshinobu of the Foundations of Mathematical Informatics group studies foundations of mathematics, in particular axiomatic set theory.
Set theory takes as its starting point the fact that infinite sizes (cardinalities) come in many kinds, and seeks to clarify their combinatorial properties.
Professor Yoshinobu is interested in using large cardinal axioms to classify infinitary combinatorial statements of set theory by the yardstick of consistency strength.
On Professor Yoshinobu's page, it is stated that anyone wishing to specialize in this field needs to be thoroughly familiar with the logical and abstract way of thinking in mathematics.
Key terms
- Cardinality
- The notion of expressing the size of a set. Cantor pointed out that infinite sets also come in many different sizes.
- ZFC
- The axiom system of set theory developed by Zermelo, Fraenkel, and others. Most set theorists work within this system.
- Large cardinal axiom
- An axiom that assumes the existence of huge infinite cardinals with very strong properties. The larger the cardinal, the stronger the consistency claim becomes.
ResearchResearch themes
There are problems that cannot be decided by ZFC, the axiom system of set theory, alone, and large cardinal axioms have been considered as a way toward resolving them. Professor Yoshinobu is interested in classifying infinitary combinatorial statements by the yardstick of consistency strength.
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MembersFaculty
- ProfessorYasuo Yoshinobu
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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: “04fig-venn-002” ASpiegler / CC BY-SA 4.0 (cropped)
- Large Cardinal Axioms and Infinitary Combinatorics: “Math01” MathKnight ✡ (Talk) No machine-readable author provided. MathKnight assumed (based on copyright claims). / CC BY 2.5 (cropped)
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