Definition

Let A be an object. Then we say A is a limit ordinal if "A is an ordinal"∧∀a∈A⋅∃b∈A⋅a∈b.

Background

The following background is necessary to understand this definition.

(.) Let A and x be objects. Then x∈A is a proposition.

(.) Let φ and ψ be propositions. Then φ∧ψ is a proposition.

(.) Let A be an object. Let φ(a) be a proposition depending on a member a of A. Then "∀a∈A⋅φ(a)" is a proposition.

(.) Let A be an object. Let φ(a) be a proposition depending on a member a of A. Then "∃a∈A⋅φ(a)" is a proposition.

(.) Let x be an object. Then "x is an ordinal" is a proposition.

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