Skolem Theories
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In general, if is a theory and for each formula with free variables there is a Skolem function, then is called a Skolem theory. For example, by the above, arithmetic with the Axiom of Choice is a Skolem theory.
Every Skolem theory is model complete, i.e. every substructure of a model is an elementary substructure. Given a model M of a Skolem theory T, the smallest substructure containing a certain set A is called the Skolem hull of A. The Skolem hull of A is an atomic prime model over A.
Read more about this topic: Skolem Normal Form
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“Generalisation is necessary to the advancement of knowledge; but particularly is indispensable to the creations of the imagination. In proportion as men know more and think more they look less at individuals and more at classes. They therefore make better theories and worse poems.”
—Thomas Babington Macaulay (1800–1859)