You should only ask practical, answerable questions based on actual problems that you face. Chatty, open-ended questions diminish the usefulness of our site and push other questions off the front page
(from our help on asking questions).
The set theory/correlation question strikes me as being of this type. I said as much in comments, but because the space for explanations is limited there, here I will elaborate a little.
Set theory is fundamental to mathematics, so it would not be unfair to draw some parallels between the subject question and hypothetical questions one can think of asking about how correlation (or some other statistical concept) might be "related" to, say, addition or logic or real numbers. These hypotheticals might help make the breadth and vagueness of such questions more apparent. In particular,
What form of "correlation" do you have in mind? Pearson, Spearman, Kendall's Tau, etc.? Some generic concept of "linear relation"? Or even a broad concept of "statistically related"?
What kind of "relation" are you considering and why might it be important? Many correlation coefficient formulas involve addition in some form, but in most cases it's doubtful this sheds any light either on the concept of correlation or of addition.
Addition can be exploited in many different ways, according to the many different formulas for the many different forms of correlation. Which way is of interest and why?
Another problem with the original question is that if such questions were considered on-topic here, we would open ourselves to moderating and curating an endless number of vague, open-ended questions of the form "is there any relation between [broad mathematical concept X] and [broad statistical concept] Y?" No such question is sufficiently specific and focused to be appropriate here on CV.
For more guidance, please read the remainder of the help page I cited.