Basic Universe is not Set
Jump to navigation Jump to search
Let $V$ be a basic universe.
Then $V$ is not a set.
That is, $S \in V$.
This contradicts the deduction that $S \notin V$.
Hence the result by Proof by Contradiction.
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 2$ Transitivity and supercompleteness