## Colloquium

Seminar information archive ～05/21｜Next seminar｜Future seminars 05/22～

Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
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URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html |

**Future seminars**

### 2024/05/31

15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

Introduction to large cardinals (JAPANESE)

https://forms.gle/ZmHhZW6bxUyKewro8

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

**Hiroshi Sakai**(Graduate School of Mathematical Sciences, The University of Tokyo)Introduction to large cardinals (JAPANESE)

[ Abstract ]

Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.

[ Reference URL ]Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.

https://forms.gle/ZmHhZW6bxUyKewro8