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computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.
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Does the exact pair phenomenon for partial orders occur in your area of mathematics?
Rather than an answer, a comment that is too long to go where it belongs.
I'm guessing that this phenomenon is rarely observed, because mathematicians neither want to nor have much reason to deal wit …