Mathematical Logic Quarterly 47 (3):305-314 (2001)

Abstract
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
Keywords Quotient fields  Fragments of Arithmetic  Restricted ultraproducts
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DOI 10.1002/1521-3870(200108)47:3
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