Zermelosystem

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A Zermelosystem denotes a subset system in set theory and originates from Ernst Zermelo's proof of the comparability theorem .

A set is called a chain of subsets (⊆-chain) if:

A non-empty set is called a Zermelosystem if for all ⊆-chains in :

Be a Zermelosystem, it means a goal of when:

One can use the axiom of choice to prove that such a goal exists in any Zermelosystem.

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