Category:Definitions/Basic Universe

From ProofWiki
Jump to navigation Jump to search

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 $\ds \bigcup x$ is also a set.


$\text A 6$: Axiom of Powers

Let $x$ be a set.

Then its power set $\powerset x$ is also a set.

Pages in category "Definitions/Basic Universe"

The following 3 pages are in this category, out of 3 total.