AbstractWe 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 under the assumption κ<κ = κ. Our main result is actually proved in a stronger form which covers also L∞κ (and makes sense there) for every strong limit cardinal λ < κ of cofinality κ.