202602102159

Tags : Model Theory

ACFp is $\kappa$ categorical for uncountable $\kappa$

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Two algebraicaly closed fields are isomorphic iff they have the same characteristic and transcendence degree.

The cardinality of the an algebraically closed field is $\lambda +{\aleph }_0$ where $\lambda$ is the transcendence degree. Therefore if algebraically closed field has an infinite cardinality $\kappa$ iff its transcendence degree is $\alpha$

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References

• Theory of torsion-free divisible Abelian Groups is kappa categorical for uncountable kappa