There are also basis theorems for lightface formula 2 sets. It includes the study of lightface pointclasses, and is closely related to hyperarithmetical theory. This produces that hyperarithmetic hierarchy, which is the lightface analog of the Borel hierarchy. Each lightface Borel set has infinitely many distinct codes. Its lightface analog is known as the analytical hierarchy. In particular, it focuses on lightface analogues of hierarchies of classical descriptive set theory. The lightface Borel hierarchy can be defined on any effective Polish space. The lightface Borel hierarchy is an effective version of the boldface Borel hierarchy. The Greek letters here are lightface symbols, which indicate this choice of language. The lightface Borel hierarchy extends the arithmetical hierarchy of subsets of an effective Polish space.