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Quotient Fields of a Model of IΔ 0 + Ω 1
Author(s) -
D'Aquino Paola
Publication year - 2001
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200108)47:3<305::aid-malq305>3.0.co;2-4
Subject(s) - quotient , mathematics , principal ideal , ideal (ethics) , ideal class group , prime ideal , finite field , field (mathematics) , pure mathematics , prime (order theory) , degree (music) , discrete mathematics , algebraic number , maximal ideal , combinatorics , mathematical analysis , physics , philosophy , epistemology , acoustics
In [4] the authors studied the residue field of a model M of IΔ 0 + Ω 1 for the principal ideal generated by a prime p . One of the main results is that M /< p > 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.