Russell's Paradox - Formal Presentation

Formal Presentation

Define Naive Set Theory (NST) as the theory of predicate logic with a binary predicate and the following axiom schema of unrestricted comprehension:

for any formula P with only the variable x free. Substitute for . Then by existential instantiation (reusing the symbol y) and universal instantiation we have

a contradiction. Therefore NST is inconsistent.

Read more about this topic:  Russell's Paradox

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