7 articles
Atomic model (model theory)
In model theory, an atomic model is a model of a first-order theory whose every realized type is isolated by a single formula, making it a small model.
Existentially closed model
An existentially closed model, also called an existentially complete model, is a model of a theory that already solves every existential condition solvable in an extension.
Generic structure
A generic structure, also called a Fraïssé limit or rich model, is a countable homogeneous structure containing every finite structure from a given class, unique up to isomorphism.
Model companion
A model companion of a first-order theory T is a model complete theory whose models each embed in models of T and vice versa, introduced by Abraham Robinson.
Model theory
Model theory, also called the theory of models, is the branch of mathematical logic studying how formal languages are interpreted, especially first-order languages and their structures.
Prime model
A prime model in model theory is a model that can be elementarily embedded into every other model of its complete theory, a notion Robert Vaught introduced in 1961.
Saturated model
A saturated model, also called a saturated structure, is a model of a first-order theory realizing every type over smaller parameter sets, a key concept from Morley and Vaught's 1962 paper.