Quotient Fields of a Model of IΔ0 + Ω1.

In [4] the authors studied the residue field of a model M of IΔ₀ + Ω₁ for the principal ideal generated by a prime p. One of the main results is that M/ has a unique extension of each finite degree. In this paper we are interested in understanding the structure of any quotient field of M, i.e. we will study the quotient M/I for I a maximal ideal of M. We prove that any quotient field of M satisfies the property of having a unique extension of each finite degree. We will use some of Cherlin's ideas from [3], where he studies the ideal theory of non standard algebraic integers. [ABSTRACT FROM AUTHOR]