Predicate Exchangeability and Language Invariance in Pure Inductive Logic

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 \${\textbackslash}phi\$ according to this permutation should not change our belief in the truth of \${\textbackslash}phi\$. In this paper we study when a probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfi?es the principle of Unary Language Invariance.