*This may be a very naive question which only reflects my failure at literature search, but:*

Although realizability (in its original form at least) is grounded in computability, the details of computability theory itself don't seem too relevant for realizability as far as I can tell. For example, I don't know of any result in realizability which relies on (say) the Low Basis Theorem or on the solution to Post's problem. Basic computability of course plays a role - e.g. whipping up realizability semantics appropriate for computability notions which lack universal machines, such as the primitive recursive functions, is difficult and interesting - but *(to my practically-nonexistent knowledge)* the deeper results don't seem to play a role.

**My question is whether this is accurate**. In particular, I'd be extremely interested in any significant role played by *priority arguments* in realizability.

The most relevant thing I've found is Charles McCarty's paper "Realizability and recursive set theory", which established a connection between isols/recursive equivalence types and realizability. There are many results about isols, of course, which are proved via complicated priority arguments. However, unless I'm missing something this seems to be a situation where realizability sheds light on the isols, rather than results about isols being relevant to realizability.

outsideof mathematical logic), and even then I think that's rather overstated. If you're trying to infer that computability theory isn't useful outside of computability theory, that's just false - consider e.g. the role of hyperarithmeticity in proving the Harrington-Kechris-Louveau theorem. $\endgroup$ – Noah Schweber May 9 at 16:07