In set theory, a universal set is a set which contains all objects, including itself.Forster 1995 p. 1. The most widely-studied set theory with a universal set is Willard Van Orman Quine’s New Foundations, but Alonzo Church and Arnold Oberschelp also published work on such set theories. Church speculated that his theory might be extended in a manner consistent with Quine’s,Church 1974 p. 308, but see also Forster 1995 p. 136 or 2001 p. 17. but this is not possible for Oberschelp’s, since in it the singleton function is provably a set,Oberschelp 1973 p. 40. which leads immediately to paradox in New Foundations.
