Some articles on grothendieck universes, grothendieck universe, universe:
Category Of Sets - Foundations For The Category of Sets
... Another solution is to assume the existence of Grothendieck universes ... Roughly speaking, a Grothendieck universe is a set which is itself a model of ZF(C) (for instance if a set belongs to a universe, its elements and its powerset will belong to the universe) ... The existence of Grothendieck universes (other than the empty set and the set of all hereditarily finite sets) is not implied by the usual ZF axioms ...
... Another solution is to assume the existence of Grothendieck universes ... Roughly speaking, a Grothendieck universe is a set which is itself a model of ZF(C) (for instance if a set belongs to a universe, its elements and its powerset will belong to the universe) ... The existence of Grothendieck universes (other than the empty set and the set of all hereditarily finite sets) is not implied by the usual ZF axioms ...
Grothendieck Universes and Inaccessible Cardinals
... There are two simple examples of Grothendieck universes The empty set, and The set of all hereditarily finite sets ... Loosely speaking, this is because Grothendieck universes are equivalent to strongly inaccessible cardinals ... two axioms are equivalent (U) For each set x, there exists a Grothendieck universe U such that x ∈ U ...
... There are two simple examples of Grothendieck universes The empty set, and The set of all hereditarily finite sets ... Loosely speaking, this is because Grothendieck universes are equivalent to strongly inaccessible cardinals ... two axioms are equivalent (U) For each set x, there exists a Grothendieck universe U such that x ∈ U ...
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