Archive for Mathematical Logic

, Volume 49, Issue 6, pp 693–723 | Cite as

Saturated models in institutions

Article

Abstract

Saturated models constitute one of the powerful methods of conventional model theory, with many applications. Here we develop a categorical abstract model theoretic approach to saturated models within the theory of institutions. The most important consequence is that the method of saturated models becomes thus available to a multitude of logical systems from logic or from computing science. In this paper we define the concept of saturated model at an abstract institution-independent level and develop the fundamental existence and uniqueness theorems. As an application we prove a general institution-independent version of the Keisler–Shelah isomorphism theorem “any two elementarily equivalent models have isomorphic ultrapowers” (assuming Generalized Continuum Hypothesis).

Keywords

Saturated models Institutions Institution-independent model theory 

Mathematics Subject Classification (2000)

03C50 03C95 18C50 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  2. 2.Şcoala Normală Superioară BucureştiBucharestRomania

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