"The core members include A, B, C and D"
Does this imply that there are still other core member(s)? Or the reader thinks that there are four members and that's all? Or could it be interpreted in both ways?
This doesn't imply anything about the existence of other core members. There might be more; there might not be. Writing the sentence this way is ONLY a good idea if you deliberately want to be vague about whether or not there are any other core members.
In formal (especially legal) language, you will often see the phrase "including, but not limited to A, B, C, and D" which suggests more strongly that there MIGHT be others (but still doesn't assert that there definitely are).
You can also say, "The core members include A,B,C, and D only" if you want to rule out the possibility of any other core members. In that sentence, though, it would be better to just say "The core members ARE A, B, C, and D."
And you can say "The core members include A,B,C and D, among others," if you want to say for certain that there are other core members.