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I love compatibility theory, degree theory etc and I'm astonished by the advances that have been made in the field but it often seems like computability is less cumulative than other areas of mathematics. I get the sense that it other fields it's more common to establish a result in a way that merely uses other results but doesn't require you to dig into their proofs.

Is it really true that computability theory is less cumulative in something like this sense? If so is this some essential aspect of the subject or just because it's still quite a young field? For instance, iin 100 years should we expect computability theory to look mostly the same with just more construction techniques and more kinds of notions to explore or be transformed by methods that let one indirectly prove results without directly managing ever more complexity?

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    $\begingroup$ I don't think it is possible to predict with confidence what any field will look like in 100 years $\endgroup$
    – Will Sawin
    Commented Oct 14, 2022 at 2:10
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    $\begingroup$ Not the only field where this feeling is present: mathoverflow.net/q/15292/6085 $\endgroup$
    – Andrés E. Caicedo
    Commented Oct 14, 2022 at 2:12
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    $\begingroup$ @Ben Burns: Perhaps by "less cumulative" is meant "more hair", to use a phase that I recall used from time to time (mid 1970s to maybe mid 1990s; haven't heard it used much in more recent times, and I also can't seem to find it used this way online) for especially icky and highly technical "down and dirty" constructions and proofs. And if not, then I certainly would characterize many of the proofs as having a lot of hair, which doesn't take an expert (which I'm certainly not) to recognize. $\endgroup$
    – Dave L Renfro
    Commented Oct 14, 2022 at 2:26
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    $\begingroup$ @BenBurns Yes, done. I mean something like what you say but you could imagine that proofs remain dirty but they somehow are able to prove more general results. For instance, lots of forcing proofs in set theory are dirty constructions but they aren't just straight building up a model to demonstrate consistency. I'd call that cumulative even though proofs are no less intricate bc they prove much more with that given lvl of detail. $\endgroup$
    – Peter Gerdes
    Commented Oct 14, 2022 at 4:31
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    $\begingroup$ @DaveLRenfro, the preface to the 3d (1989) edition of Boolos and Jeffrey’s Computability and Logic mentions that kind of hair. $\endgroup$
    – user44143
    Commented Oct 16, 2022 at 9:14

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