Abstract: 

It is well-known that an algebraically closed field can not be an ordered field. But it can be equipped with a multiplicative circular order. For example, we can define a multiplicative circular order on an algebraic closure of a finite prime field using an injective multiplicative character. C. M. Tran initiated study of algebraically closed fields with a multiplicative circular order. Especially. he characterized the theory of such fields, denoted by ACFO, and ACFO is decidable. In this talk, we will show that algebraically closed fields with multiplicative circular orders satisfy the amalgamation property, which does not hold for ordered fields.

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