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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“Our books of science, as they improve in accuracy, are in danger of losing the freshness and vigor and readiness to appreciate the real laws of Nature, which is a marked merit in the ofttimes false theories of the ancients.”
—Henry David Thoreau (1817–1862)