Set theory MOC

Russell's paradox

Russell's paradox states that the Russellian Class 𝑅 defined by

(∀𝔐⁡𝑥)[𝑥∈𝑅⟺𝑥∉𝑥]

is not a set. #m/thm/set For if it were a set, either 𝑅 ∈𝑅 or 𝑅 ∉𝑅 implies its opposite, which is absurd. The main issue at hand is unrestricted comprehension, and different approaches to axiomatic set theory must take care to resolve this paradox.

#state/tidy | #lang/en | #SemBr