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# example of universe

The simplest example of a universe consists of all sets gotten by starting with the empty set and repeatedly aggregating sets already known to lie in the universe. That is to say, starting with $\emptyset$, we first form $\{\emptyset\}$. Given these two elements of our universe, we can then form $\{\{\emptyset\}\}$ and $\{\emptyset,\{\emptyset\}\}$. Given these four elements, we then can form $\{\{\{\emptyset\}\}\}$, $\{\emptyset,\{\{\emptyset\}\}\}$, $\{\{\emptyset,\{\emptyset\}\}\}$ and several other sets. We can repeat this process to obtain an infinite collection of finite sets.

The set considered here also happens to be the set $V_{\omega}$ in the cumulative hierarchy.

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CumulativeHierarchy

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Example

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## Mathematics Subject Classification

18A15*no label found*03E30

*no label found*

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