Lachlan on topology for priority arguments

Question

There is a set of notes by Lachlan from 1973 on casting priority arguments in topological language; references to these notes are few and far between, but one source refers to them as "Topology for Priority Arguments," which for now I'll assume is the title. Regardless, they seem to have never been published; my understanding is that their line of inquiry never caught on.

I did see them long ago, in a computability theory class; and I've recently become re-interested in them. The instructor, unfortunately, no longer has a copy. I was wondering if anyone knew how I could find these notes, or had a copy.

Answer 1

After about my third priority argument in a graduate class, I too was interested in finding a general approach for handling them. You can find something similar from Lachlan in published form as The priority method for the construction of recursively enumerable sets in Lecture Notes in Mathematics 337.

The most developed general framework for priority arguments is A framework for priority arguments by Lerman. It's more order-theoretic than topological, but I doubt it would be too difficult to recast it in topological language.