ORDINAL NUMBERS IN ARITHMETIC PROGRESSION
β Scribed by Frederick Bagemihl; F. Bagemihl
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 209 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
The class of all ordinal numbers can be partitioned into two subclasses in such a way that neither subclass contains an arithmetic progression of order type Ο, where an arithmetic progression of order type Ο means an increasing sequence of ordinal numbers (Γ + δγ)Ξ³<Ξ³<>r, Ξ΄ β 0.
π SIMILAR VOLUMES
We show that if G is a K r -free graph on N, there is an independent set in G which contains an arbitrarily long arithmetic progression together with its difference. This is a common generalization of theorems of Schur, van der Waerden, and Ramsey. We also discuss various related questions regarding
~roughout this paper we use the following notatians: The cardinality of the finite set Y is denoted by ISI -.s& B8, . I s den&e finite or infinite sets of positive integers. If & is a finite or infinite set of positive integers, then S(d) denotes the set of the distinct positive integers n that can