Saturated models in institutions |
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Authors: | Răzvan Diaconescu Marius Petria |
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Affiliation: | 1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Bucharest, Romania 2. ?coala Normal? Superioar? Bucure?ti, Bucharest, Romania
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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). |
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