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 … See more

The theorem was conjectured by Andrew Vázsonyi and proved by Joseph Kruskal (1960); a short proof was given by Crispin Nash-Williams (1963). It has since become a prominent example in reverse mathematics as … See more

For a countable label set X, Kruskal's tree theorem can be expressed and proven using second-order arithmetic. However, like Goodstein's theorem or the Paris–Harrington theorem, some special cases and … See more

Suppose that is the statement:
There is some m such that if T1, ..., Tm is a finite sequence of unlabeled rooted trees where Ti has vertices, then for some .
All the statements are true as a consequen… See more

• Paris–Harrington theorem
• Kanamori–McAloon theorem
• Robertson–Seymour theorem See more

Friedman originally denoted this function by TR[n]. n(k) is defined as the length of the longest possible sequence that can be constructed with a k-letter alphabet such that no block of letters xi,...,x2i is a subsequen… See more