Tree (descriptive set theory): Difference between revisions

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===Trees===

The collection of all finite sequencesequences of elements of a set <math>X</math> is denoted <math>X^{<\omega}</math>.

With this notation, a tree is a nonempty subset <math>T</math> of <math>X^{<\omega}</math>, such that if

<math>\langle x_0,x_1,\ldots,x_{n-1}\rangle</math> is a sequence of length <math>n</math> in <math>T</math>, and if <math>0\le m<n</math>,