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1. • CommentRowNumber1.
   • CommentAuthorjesse
   • CommentTimeSep 5th 2016
   • (edited Sep 5th 2016)
   • PermaLink
   Author: jesse
   Format: MarkdownItexAs promised [in this thread](https://nforum.ncatlab.org/discussion/7259/type-in-model-theory), I've written up how model theorists treat Galois theory at [[model-theoretic Galois theory]]. I briefly mention the connection with the theory of internal covers and the [[Tannaka duality|Tannakian formalism]]. The proof of the fundamental order-reversing bijection between closed subgroups and intermediate extensions is essentially Poizat's, but I don't mention the corresponding Galois theory for the strong Stone space (types taken in $T^{\operatorname{eq}}$), which is the language he prefers. I've also filled out necessary references at [[monster model]], [[model-theoretic algebraic closure]], and [[theory of algebraically closed fields]].

   As promised in this thread, I’ve written up how model theorists treat Galois theory at model-theoretic Galois theory. I briefly mention the connection with the theory of internal covers and the Tannakian formalism. The proof of the fundamental order-reversing bijection between closed subgroups and intermediate extensions is essentially Poizat’s, but I don’t mention the corresponding Galois theory for the strong Stone space (types taken in $T^{\operatorname{eq}}$), which is the language he prefers.

   I’ve also filled out necessary references at monster model, model-theoretic algebraic closure, and theory of algebraically closed fields.