# Paris–Harrington theorem (Q7137494)

states that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, is true, but not provable in Peano arithmetic
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Paris–Harrington theorem
states that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, is true, but not provable in Peano arithmetic

## Statements

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${\displaystyle {\binom {N}{n}}=|{\mathcal {P}}_{n}(S)|\geq R(\,\underbrace {m,m,\ldots ,m} _{k}\,)}$
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