# Talk:Tree (descriptive set theory)

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Field: Foundations, logic, and set theory

## closed under "subsequence"?

subsequence can be more general than a truncated sequence with coinciding initial parts. Subsequence might include consecutive terms, not necessarily beginning with the sequence's first term. It is used in other areas of mathematics to mean a sequence obtained by omitting any number of elements from the original sequence, hence they would not have to be consecutive. The beginning of this article needs to be more clear. It might read "... that is closed under truncation of the terminal end," if that is all that is meant by "closed under subsequence."24.58.63.18 (talk) 02:06, 23 February 2009 (UTC)

I definitely think you are right and I change the world "subsequences" to "initial segments". (Which is the term that is common in descriptive set theory for this.) --Kompik (talk) 08:03, 18 October 2009 (UTC)

## cartesian products

$(X\times Y)^{\omega }\cong X^{\omega }\times Y^{\omega }$ this is natural. Was

$(X\times Y)^{{<\omega }}$ is naturally identified with a subset of $X^{{<\omega }}\times Y^{{<\omega }}$


what was meant? 24.58.63.18 (talk) 02:21, 23 February 2009 (UTC)