Journal of Applied Logic
Volume 3, Issue 1, March 2005, Pages 15-41

http://www.sciencedirect.com/science/article/pii/S1570868304000503
The most popular of those is the so-called Russell set, R := {x|not x∈x}, for by the law of
excluded middle one immediately gets ‘R∈R∧not R∈R’, an apparent contradiction.