Round 9: 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. (10[1]-5[1])Gottlob Frege (“FRAY-guh”) defined numbers as these objects, which is also done in Zermelo-Frankel theory. (10[1])The naïve theory of these objects is subject to Russell’s paradox, which concerns one of these objects containing all of these objects that do not contain themselves. 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■ (10[1])

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