An Ordinal Partition from a Scale

Jean A. Larson
Additional contact information
Jean A. Larson: University of Florida, Department of Mathematics

A chapter in Set Theory, 1998, pp 109-125 from Springer

Abstract: Abstract In this paper, some theorems of Hajnal are revisited to weaken the hypothesis of CH to the existence of a short scale (∂ = N1). In particular, if ∂=N1, then there is a triangle-free graph G on ω 1 · ω such that every subset X ⊆ ω 1 2 of order type ω 1 2 has an edge. In the notation of Rado, these results may be expressed as $$partial = {N_1} \Rightarrow \omega _1^2 \to {\left( {\omega _1^2,3} \right)^2}$$ and $$\partial = {N_1} \Rightarrow {\omega _1} \cdot \omega \to {\left( {{\omega _1} \cdot \omega ,3} \right)^2}$$ These results are generalized to partition relations for k · λ and k 2, when λ is regular and k = λ+.

Keywords: Limit Point; Order Type; Small Fiber; Regular Cardinal; Partition Relation (search for similar items in EconPapers)
Date: 1998
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-8988-8_8

Ordering information: This item can be ordered from
http://www.springer.com/9789401589888

DOI: 10.1007/978-94-015-8988-8_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().