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 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 subsequence of any later block xj,...,x2j. See more

For a countable label set X, Kruskal's tree theorem can be expressed and proven using second-order arithmetic. However, like See more

Suppose that $${\displaystyle P(n)}$$ is the statement:
There is some m such that if T1, ..., Tm is a finite sequence of … See more