We seek conditions for the exchangeable $\sigma$-field of an independent non-identically-distributed sequence of random variables to be trivial. A simple necessary condition is given, and this condition is shown to be sufficient when the range space is finite. In the case of a general range space, a stronger condition is shown to be sufficient.
"On the Zero-one Law for Exchangeable Events." Ann. Probab. 7 (4) 704 - 723, August, 1979. https://doi.org/10.1214/aop/1176994992