 Jensen (1968) showed that NFU (New Foundations with urelements), the version of New Foundations in which extensionality is weakened to allow many non-sets (as described above under naive set theory) is consistent, is consistent with Infinity and Choice, and is also consistent with the negation of Infinity (which of course implies Choice). NFU, which has the full stratified comprehension axiom of NF with all its frighteningly big sets, is weaker in consistency strength than Peano arithmetic; NFU + Infinity + Choice is of the same strength as TST with Infinity and Choice or Mac Lane set theory.