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The elementary theory of e-free PAC domains

✍ Scribed by Aharon Razon

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
290 KB
Volume
103
Category
Article
ISSN
0168-0072

No coin nor oath required. For personal study only.

✦ Synopsis

We prove that the theory of all sentences in the language of rings which are true in Z ∩ Q( ) for almost all ∈ G(Q) e is decidable. Here Q is the ÿeld of all algebraic numbers; Z is the ring of all algebraic integers; G(Q) is the absolute Galois group of Q; for each = ( 1; : : : ; e) ∈ G(Q) e , Q( ) is the ÿxed ÿeld of 1; : : : ; e in Q; and the clause 'almost all' is used in the sense of the Haar measure of G(Q) e .

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