Tree (descriptive set theory): Difference between revisions

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{{for|the concept in set theory|Tree (set theory)}}

{{technical|date=November 2013}}

In [[descriptive set theory]], a '''tree''' on a set <math>X</math> is a set of finite sequences of elements of <math>X</math> that is closed under initial segments.

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is a partial order in which each initial segment is well-ordered. The height of each sequence ''x'' is then its length, and hence finite.

Conversely, every partial order (''T'', &lt;) where each initial segment { ''y'': ''y'' < ''x''₀ } is well-ordered is isomorphic to a tree described here, assuming that all elements have finite height.

==See also==