Abstract
The complexity of priority proofs in recursion theory has been growing since the first priority proofs in [1] and [7]. Refined versions of classic priority proofs can be found in [11]. To this date, this part of recursion theory is at about the same stage of development as real analysis was in the early days, when the notions of topology, continuity, compactness, vector space, inner product space, etc., were not invented. There were no general theorems involving these concepts to prove results about the real numbers and the proofs were repetitive and lengthy.
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