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Regressive Ramsey Numbers Are Ackermannian

✍ Scribed by Menachem Kojman; Saharon Shelah

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 86 KB
Volume: 86
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2906

No coin nor oath required. For personal study only.

✦ Synopsis

We give an elementary proof of the fact that regressive Ramsey numbers are Ackermannian. This fact was first proved by Kanamori and McAloon with mathematical logic techniques.

1999 Academic Press

Nous vivons encore sous le reÁ gne de la logique, voilaÁ , bien entendu, aÁ quoi je voulais en venir. Mais les proce de s logiques, de nos jours, ne s'appliquent plus qu'aÁ la re solution de probleÁ mes d 'inte re^t secondaire (Andre Breton, Manifeste du surre alisme).

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On Regressive Ramsey Numbers

✍ Peter Floodstrand Blanchard 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 111 KB

## for my mentors don bonar and gerald thompson We prove the following relation between regressive and classical Ramsey numbers ¼ 8; R 4 reg ð6Þ ¼ 15; and R 5 reg ð7Þ536: We prove that R 2 xþk ð4Þ42 kþ1 ð3 þ kÞ À ðk þ 1Þ; and use this to compute R 2 reg ð5Þ ¼ 15: Finally, we provide the bounds 19