Adding the so-called axiom of free construction to PST, any consistent system of set-theoretical axioms will have an inner model in the resulting system. It is an unfriendly feature of PST that it cannot handle classes of sets of real numbers or classes of sets of real functions. However, it is not a necessary one. (A3) can be modified various ways to allow for various portions of the usual hierarchy of infinites, with or without supporting the continuum hypothesis. One example is In this version, the cardinality of an infinite set is either or , and the cardinality of a proper class is (which means that the generalized continuum hypothesis holds). See also Large cardinal Notes References External links Randall Holmes: Notes on "Pocket Set Theory" Systems of set theory