About: Honest leftmost branch

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In set theory, an honest leftmost branch of a tree T on ω × γ is a branch (maximal chain) ƒ ∈ [T] such that for each branch g ∈ [T], one has ∀ n ∈ ω : ƒ(n) ≤ g(n). Here, [T] denotes the set of branches of maximal length of T, ω is the smallest infinite ordinal (represented by the natural numbers N), and γ is some other ordinal.

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  • In set theory, an honest leftmost branch of a tree T on ω × γ is a branch (maximal chain) ƒ ∈ [T] such that for each branch g ∈ [T], one has ∀ n ∈ ω : ƒ(n) ≤ g(n). Here, [T] denotes the set of branches of maximal length of T, ω is the smallest infinite ordinal (represented by the natural numbers N), and γ is some other ordinal. (en)
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  • In set theory, an honest leftmost branch of a tree T on ω × γ is a branch (maximal chain) ƒ ∈ [T] such that for each branch g ∈ [T], one has ∀ n ∈ ω : ƒ(n) ≤ g(n). Here, [T] denotes the set of branches of maximal length of T, ω is the smallest infinite ordinal (represented by the natural numbers N), and γ is some other ordinal. (en)
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  • Honest leftmost branch (en)
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