Are there textbooks on logic where the references to set theory appear only after the construction of set theory?

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In textbooks on logic the authors usually use the notions of set and map immediately, long before the set theory is constructed. That is strange for me, and I want to ask if anybody can advise me a textbook on logic with a "linear structure", without these "circles in definitions"?

EDIT. This question is a reference request, so I hope, if I cross post it to MathOverflow, this will not cause a duplication of efforts for people who plan to post answers. Here is this question at MO.