![field theory - Is dependent choice what one must use in this step of Artin's construction of the algebraic closure? - Mathematics Stack Exchange field theory - Is dependent choice what one must use in this step of Artin's construction of the algebraic closure? - Mathematics Stack Exchange](https://i.stack.imgur.com/7VfvN.png)
field theory - Is dependent choice what one must use in this step of Artin's construction of the algebraic closure? - Mathematics Stack Exchange
I learned in Galois Theory that any field can be algebraically closed, with the proof using Zorn's Lemma. Is the algebraic closure of a finite field recognizable in any sense, like the
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PDF) Quantifier Elimination over Algebraically Closed Fields in a Proof Assistant using a Computer Algebra System
![abstract algebra - Operator generating subuniverse generated by X is algebraic closure operator - Mathematics Stack Exchange abstract algebra - Operator generating subuniverse generated by X is algebraic closure operator - Mathematics Stack Exchange](https://i.stack.imgur.com/PAqVD.png)
abstract algebra - Operator generating subuniverse generated by X is algebraic closure operator - Mathematics Stack Exchange
![abstract algebra - Proof that every field $F$ has an algebraic closure $\bar F$ - Mathematics Stack Exchange abstract algebra - Proof that every field $F$ has an algebraic closure $\bar F$ - Mathematics Stack Exchange](https://i.stack.imgur.com/fcGL8.png)