We prove that the class of trees with no branches of cardinality ≥κ is not RPC definable in L ∞κ when κ is regular. Earlier such a result was known for L κ + κ under the assumption $\kappa^{ . Our main result is actually proved in a stronger form which covers also L ∞λ (and makes sense there) for every strong limit cardinal $\lambda > \kappa$ of cofinality κ.