## Coding complete theories in Galois groups.(English)Zbl 1146.03019

For a topological space $$X$$ we denote by $$\mathcal{C}(X)$$ the set of closed, non-empty subsets of $$X.$$ The Vietoris space of $$X,$$ denoted $$\mathcal{V}(X)$$, is the topology on $$\mathcal{C}(X)$$ with basic open sets $$\langle U_1,\dots,U_{n}\rangle:= \{C\in \mathcal{C}(X):C\subseteq \bigcup U_{i},i=1,\dots,k$$ and $$C\cap U_{i}\neq \emptyset$$ for $$i=1,\dots,k\}$$ for each finite collection $$U_{1},\dots,U_{n}$$ of open sets of $$X.$$ In this paper the author give a new characterization of the spaces of complete theories of pseudo-finite fields and of algebraically closed fields with a generic automorphism in terms of the Vietoris topology on absolute Galois groups of prime fields.

### MSC:

 03C60 Model-theoretic algebra 12L12 Model theory of fields
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### References:

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