About apparent circularity in logic and set theory

Question

This is more of a question about philosophy of mathematics. There is an apparent circularity in set theory and logic, in the means that we use set theory to define model theory, and we use results from model theory for proofs in set theory. And, analogously, we use set theory to prove facts from logic (unique readability, for example) and we define set theory using logic. I feel that we can reduce all this notions to a single syntactical idea of logical consequence, and from there we can define things in a non-circular way. However, I can't seem to make this notions all fit together in a logical, foundational manner. Does anyone know of an article or book that addresses this issue?