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:*I agree that we aren't talking about set theory — for "class of functions" substitute "kind of function", if you like. The kind of function computed by the various models are all the same, and are treated at [[computable function]]. The differences in model of computation are "implementation details", like different programming languages if you will.
:*The point about including the computation as part of the function in some sense is generally well-taken, but doesn't really change anything in this discussion. The computation that computes a given function can be effectively translated between different models of computation in a completely stereotyped way, and you can prove using very mild assumptions (and I'm pretty sure, even in intuitionistic logic) that they compute the same function. Therefore we can still speak of whether a computable function is provably total (for example) without worrying about which model of computation is used.
:Well, that's a lot, better stop here. The big takeaway is we should move this content to a name that clearly names a model of computation, for example [[μ-recursion]], and all the "function" links should point at [[computable function]]. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 21:18, 24 February 2020 (UTC)
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