Category:Grothendieck Universes
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This category contains results about Grothendieck Universes.
A Grothendieck universe is a set (not a class) which has the properties expected of the universe $\mathbb U$ of sets in the sense of the Zermelo-Fraenkel axioms with the following properties:
- $(1): \quad \mathbb U$ is a transitive set: If $u \in \mathbb U$ and $x \in u$ then $x \in \mathbb U$
- $(2): \quad$ If $ u, v \in \mathbb U$ then $\set {u, v} \in \mathbb U$
- $(3): \quad$ If $u \in \mathbb U$ then the power set $\powerset u \in \mathbb U$
Pages in category "Grothendieck Universes"
The following 6 pages are in this category, out of 6 total.