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)
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: "@stubborncurias @wtgowers Briefly, Ramsey theory is connected to functions that grow so fast they can't be understood using Peano arithmetic! The proof of the Paris-Harrington theorem, sketched John Carlos Baez on Twitter: "@stubborncurias @wtgowers Briefly, Ramsey theory is connected to functions that grow so fast they can't be understood using Peano arithmetic! The proof of the Paris-Harrington theorem, sketched](https://pbs.twimg.com/media/D768tzBVUAIryIf.jpg)