  In Pure Inductive Logic, the rational principle of Predicate Exchangeability
states that permuting the predicates in a given language L and replacing each
occurrence of a predicate in an L-sentence $\phi$ according to this permutation
should not change our belief in the truth of $\phi$. In this paper we study
when a probability function w on a purely unary language L satisfying Predicate
Exchangeability also satisfies the principle of Unary Language Invariance.
