Abstract
A model for a complete first order theory T in a language of finite type is minimally saturated if it is recursively saturated and elementarily embeddable in every recursively saturated model of T. Such a model is unique when it exists, and may be regarded as the smallest model of T with saturation properties. (Alternatively, if T* denotes the theory obtained from T by adding all Σ 11 -sentences consistent with T, then a minimally saturated model for T is simply a prime model for T*). We show that the existence of such a model is implied by the existence of a countably saturated model, and in turn implies the existence of a prime model, and that both these implications are strict. We also give an easily applicable sufficient condition for T to have no minimally saturated model. §3 includes a general result about the degrees of complete types of first-order theories.
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© 1980 Springer-Verlag
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Wilmers, G. (1980). Minimally saturated models. In: Pacholski, L., Wierzejewski, J., Wilkie, A.J. (eds) Model Theory of Algebra and Arithmetic. Lecture Notes in Mathematics, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090175
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DOI: https://doi.org/10.1007/BFb0090175
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