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In [[set theory]], an '''honest leftmost branch''' of a [[ |
In [[set theory]], an '''honest leftmost branch''' of a [[Tree (set theory)|tree]] ''T'' on ω × γ is a branch ([[maximal element|maximal]] [[Chain (order theory)|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 [[ordinal number|ordinal]] (represented by the [[natural number]]s '''N''') and γ is some other ordinal. |
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==See also== |
==See also== |
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Revision as of 14:36, 2 June 2016
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 ordinal (represented by the natural numbers N) and γ is some other ordinal.
See also
References
- Akihiro Kanamori, The higher infinite, Perspectives in Mathematical Logic, Springer, Berlin, 1997.
- Yiannis N. Moschovakis, Descriptive set theory, North-Holland, Amsterdam, 1980.
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