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TREE.
Last seen on: Daily Crossword Club Crossword Answers Wednesday, March 15, 2023
Random information on the term “TREE”:
In mathematical logic, the Paris–Harrington theorem states that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, which is expressible in Peano arithmetic, is not provable in this system. The combinatorial principle is however provable in slightly stronger systems.
This result has been described by some (such as the editor of the Handbook of Mathematical Logic in the references below) as the first “natural” example of a true statement about the integers that could be stated in the language of arithmetic, but not proved in Peano arithmetic; it was already known that such statements existed by Gödel’s first incompleteness theorem.
The strengthened finite Ramsey theorem is a statement about colorings and natural numbers and states that:
Without the condition that the number of elements of Y is at least the smallest element of Y, this is a corollary of the finite Ramsey theorem in K P n ( S ) {\displaystyle K_{{\mathcal {P}}_{n}(S)}} , with N given by: