Kruskal tree theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-02-18

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem


00:00:51 1 Statement
00:05:50 2 Weak tree function
00:06:19 3 Friedman's work
00:06:42 3.1 TREE(3)
00:08:14 4 See also
00:09:09 5 Notes
00:10:29 6 References
00:10:45 Notes
00:11:16 3, n(2)



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SUMMARY
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In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding. The theorem was conjectured by Andrew Vázsonyi and proved by Joseph Kruskal (1960); a short proof was given by  Nash-Williams (1963). It has since become a prominent example in reverse mathematics as a statement that cannot be proved within ATR0 (a form of arithmetical transfinite recursion),  and a finitary application of the theorem gives the existence of the notoriously fast-growing TREE function.
In 2004, the result was generalized from trees to graphs as the Robertson–Seymour theorem, a result that has also proved important in reverse mathematics and leads to the even-faster-growing SSCG function.