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](http://www.mathcomp.leeds.ac.uk/turing2012/inc/Talks/soareChicheley.pdf) 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.



Lachlan on topology for priority arguments
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](http://link.springer.com/chapter/10.1007/BFb0066779) in Lecture Notes in Mathematics 337.


The most developed general framework for priority arguments is [A framework for priority arguments](http://www.math.uconn.edu/~lerman/GFposet.pdf) by Lerman. It's more order-theoretic than topological, but I doubt it would be too difficult to recast it in topological language.


