There are many known ways how to make various objects definable by designing a suitable description for them with the help of forcing. One of such methods is based on so-called localization invented by R. David and further developed by S. Friedman, V. Fischer, D. Schrittesser, and many others. We shall discuss the application of this method to the study of Borel* subsets of \(2^\kappa\) for a successor cardinal \(\kappa\).
Joint work with Miguel Moreno.