Computability learning seminar

Matthew Harrison-Trainor, Pure Mathematics, University of Waterloo

"$n$-systems"

Many constructions in computability theory are priority  
arguments which build a c.e. set satisfying a list of requirements.  
The complexity of such a construction can be measured by the  
complexity of seeing how the requirements are satisfied, for example,  
finite injury arguments are $\Delta_2$. We will introduce $n$-systems,  
a general method of formalizing such constructions which is useful  
when the strategy for meeting requirements becomes very complicated.  
We will give examples of building various orderings, and show how the  
priority argument is translated into an argument using $n$-systems.