I know a fair bit about logic and none of it involves any CT. That's not to say you can't find it in there somewhere as a unifying concept, but the fundamental

I know a fair bit about logic and none of it involves any CT. That's not to say you can't find it in there somewhere as a unifying concept, but the fundamental theorems such as completeness and compactness of FOL, basic model theory, Gödel's theorems, etc. do not require any CT. Also, reflexivity, transitivity and symmetry just define an equivalence relation, no need for CT there.