User blog comment:Edwin Shade/A Complete Analysis of Taranovsky's Notation/@comment-30118230-20180129200050/@comment-32876686-20180130151122

While we're on the subject, I'd like to know, what exactly does \(\Pi^{\alpha}_{\beta}\) mean ? I am aware they refer to mathematical theories, but in what branch of mathematics, and how are they relevant to the strength of particular functions ?

(Keep in mind I am inexperienced when as it comes to set theory, so an explanation may have to omit the fine details, provided it answers the question well enough.)