The elementary theory of e-free PAC domains Original Research Article

We prove that the theory of all sentences in the language of rings which are true in View the MathML source for almost all View the MathML source is decidable. Here View the MathML source is the field of all algebraic numbers; View the MathML source is the ring of all algebraic integers; View the MathML source is the absolute Galois group of View the MathML source; for each View the MathML source, View the MathML source is the fixed field of View the MathML source in View the MathML source; and the clause ‘almost all’ is used in the sense of the Haar measure of View the MathML source.