Skolem Theories
| This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. |
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
Famous quotes containing the word theories:
“Philosophers of science constantly discuss theories and representation of reality, but say almost nothing about experiment, technology, or the use of knowledge to alter the world. This is odd, because ‘experimental method’ used to be just another name for scientific method.... I hope [to] initiate a Back-to-Bacon movement, in which we attend more seriously to experimental science. Experimentation has a life of its own.”
—Ian Hacking (b. 1936)