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Unary relations

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description: A set of unary relations Pi for i in some set I is called independent if for every two disjoint finite subsets A and B of I there is some element x such that Pi(x) is true for i in A and false for i i ...

A set of unary relations Pi for i in some set I is called independent if for every two disjoint finite subsets A and B of I there is some element x such that Pi(x) is true for i in A and false for i in B. Independence can be expressed by a set of first-order statements.

The theory of a countable number of independent unary relations is complete, but has no atomic models. It is also an example of a theory that is superstable but not totally transcendental.

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related categories

First-order theories
Large cardinal properties