We present a translation of §§160–166 of Dedekind’s Supplement XI to Dirichlet’s Vorlesungen über Zahlentheorie, which contain an investigation of the subfields of C. In particular, Dedekind explores the lattice structure of these subfields, by studying isomorphisms between them. He also indicates how his ideas apply to Galois theory. After a brief introduction, we summarize the translated exce...

We show that the absolute Galois group of a countable Hilbertian P(seudo)A(lgebraically)C(losed) field of characteristic 0 is a free profinite group of countably infinite rank (Theorem A). As a consequence, G(Q̄/Q) is the extension of groups with a fairly simple structure (e.g., ∏∞ n=2 Sn) by a countably free group. In addition, we characterize those PAC fields over which every finite group is a...