Category:Definitions/Basic Universe
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This category contains definitions related to Basic Universe.
Related results can be found in Category:Basic Universe.
A basic universe $V$ is a universal class which satisfies the following axioms:
$\text A 1$: Axiom of Transitivity
- $V$ is a transitive class.
$\text A 2$: Axiom of Swelledness
- $V$ is a swelled class.
$\text A 3$: Axiom of the Empty Set
The empty class $\O$ is a set, that is:
- $\O \in V$
$\text A 4$: Axiom of Pairing
Let $a$ and $b$ be sets.
Then the class $\set {a, b}$ is likewise a set.
$\text A 5$: Axiom of Unions
Let $x$ be a set (of sets).
Then its union $\bigcup x$ is also a set.
$\text A 6$: Axiom of Powers
Let $x$ be a set.
Pages in category "Definitions/Basic Universe"
The following 2 pages are in this category, out of 2 total.