 Given the inconsistency of unrestricted comprehension, the objective becomes to find a way to restrict either the comprehension principle itself or the underlying logical principles to regain a consistent theory, that is, a set theory that will not be trivialised by Russell’s paradox. Many alternative set theories excluding the unrestricted comprehension principle have been developed during the last century, among them the type theory of Russell and Whitehead, Simple Type theory (ST), Gödel-Bernays set theory (GB), Zermelo-Fraenkel set theory (ZF), and Quine’s New Foundations (NF). These are all believed to be consistent, although no simple proofs of their consistency are known. At least they all escape the known paradoxes of self-reference. We will return to a discussion of this in Section 3.