On a proof of undecidability of the ring of algebraic integers (Model theoretic aspects of the notion of independence and dimension)

Abstract

Let K be an algebraic extension of the rationals and A be the ring of algebraic integers of K. As to the method of proving undecidability of the ring A, it seems that the only one method has been known, which is due to Julia Robinson, especially for infinite algebraic extensions of the rationals. (See [Vi].) We discuss an alternative method for the ring of algebraic integers of cyclotomic towers for some rational primes.