This talk is an overview of Pi01 classes, which are the collections of paths through computable trees. For many years Pi01 classes have featured in the study of mathematical logic. In computability theory their study serves as a template for studying more complicated classes. Moreover, they feature as an important tool in many other areas, including, for example, the study of reverse mathematics and algorithmic randomness. Cole will give examples of important theorems and applications, describe the techniques of forcing and priority arguments used in their study, and identify some open questions of current interest.

 

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