Saturated models in institutions (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
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