Abstract
The main object of this work is to present a unified generalization of the “free generators theorem” of the author and Geyer’s theorem about the absolute Galois group of the intersection of Henselizations of a countable Hilbertian field K with respect to finitely many absolute values. We equip the absolute Galois group G(K) of K with its Haar measure and use the term “almost all” in the usual sense of measure theory.
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