It seems that the ObjectNode.PutPOJO method does not put quotes around the members of a string array,
List<String> names = List.of("Zaphod", "Arthur", "Trillian", "Ford");
ObjectMapper objectMapper = new ObjectMapper();
ObjectNode rootNode = objectMapper.createObjectNode();
rootNode.putPOJO("pojo", names);
rootNode.set("set", objectMapper.valueToTree(names));
System.out.println(rootNode);