Round 8: Tossup 7

Mereology (“mee-ree-ology”) unproblematically incorporates an analogue of these objects’ rule of unrestricted comprehension, which was originally called Basic Law V (“five”). Type theory was developed to resolve a paradox about these objects, which is often compared to a barber who can’t shave himself. Gottlob Frege (“FRAY-guh”) defined numbers as these objects, (-5[1])which is also done in Zermelo-Frankel (10[1])theory. The naïve theory of these objects is subject to Russell’s paradox, (10[1])which concerns one of these objects containing all of these objects that do not contain (10[1])themselves. (10[1])De Morgan’s laws axiomatize the union and intersection operations on these objects. (10[1])For 10 points, name these unordered collections of objects. ■END■

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