AN UNPROVABLE RAMSEY-TYPE THEOREM only. The validity of FRT* for values p , k , n , and N will be denoted in short by N -U (n)&q
![On the Proof Complexity of Paris-Harrington and Off-Diagonal Ramsey Tautologies | ACM Transactions on Computational Logic On the Proof Complexity of Paris-Harrington and Off-Diagonal Ramsey Tautologies | ACM Transactions on Computational Logic](https://dl.acm.org/cms/asset/0160c26a-0dcd-4643-a23f-81542eb5744d/2996393.cover.jpg)
On the Proof Complexity of Paris-Harrington and Off-Diagonal Ramsey Tautologies | ACM Transactions on Computational Logic
Some Bounds for the Ramsey-Paris-Harrington Numbers We first introduce some appropriate notation. Lower case variables will alwa
Some Bounds for the Ramsey-Paris-Harrington Numbers We first introduce some appropriate notation. Lower case variables will alwa
![John Carlos Baez on Twitter: "@_julesh_ However, the Paris-Harrington theorem is unprovable in PA but provable in PA + [induction up to epsilon_0]. The ordinal epsilon_0 is isomorphic to the set of John Carlos Baez on Twitter: "@_julesh_ However, the Paris-Harrington theorem is unprovable in PA but provable in PA + [induction up to epsilon_0]. The ordinal epsilon_0 is isomorphic to the set of](https://pbs.twimg.com/media/Diua3cOUYAAW0q-.jpg)