Basic Universe is not Empty
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Theorem
Let $V$ be a basic universe
Then $V$ is not the empty class.
Proof
The Axiom of the Empty Set gives us:
The empty class $\O$ is a set, that is:
- $\O \in V$
Hence the result by definition of empty class.
$\blacksquare$
Sources
- 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: $\S 3$ Axiom of the empty set