It is shown that for any directed quasi-ordered set (Q, ~<), there is a minimal ordinal number h such that every cofinal subset of Q contains a cofinal subset which is the 0-th class original set of a pure h-th class chain of Q. A special case of our results gives necessary and sufficient conditions
The Set of Better Quasi Orderings is ∏
✍ Scribed by Alberto Marcone
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 657 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper we give a proof of the II$completeness of the set of countable better quasi orderings (viewed as a subset of the Cantor space). This result was conjectured by CIote in [2] and proved by the author in his Ph.d. thesis [6] (see also [7]). Here we prove it using Simpson's definition of better quasi ordering ([15]) and as little bqo theory as possible.
Mat hematics Subject Classification: 04A 15, 03 E 15, 06A07.
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