 A much stronger system than PA, important in the foundations of mathematics, which will be mentioned now and then below, is second-order arithmetic PA\(^2\) (also often denoted by Z\(_2\)). It is more than sufficient for developing all ordinary analysis and algebra. Its language is a two-sorted first-order language (see the entry on  second-order and higher-order logic),  i.e., it contains two sorts of variables, number variables \(x_1,x_2,\ldots\) (or \(x, y, z, \ldots\)) and property variables \(X_1, X_2,\ldots\) (or \(X, Y, Z,\ldots)\), where properties are extensionally conceived. As axioms it includes, in addition to the basic axioms of PA, all instances of the second-order comprehension scheme: