Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4672891 | Indagationes Mathematicae | 2014 | 15 Pages |
Abstract
The linear ordering Rlex<Ï is the lexicographic linearization of the tree of R-valued functions defined on a finite initial segment of Ï and ordered by extension. We identify suitable notions of smallness and largeness for linear orderings that embed into Rlex<Ï by using tree representations of chains. Specifically, small linear orderings are representable by inversely well-founded trees, and large linear orderings are representable by fully uncountably branching trees. We prove the rather surprising result that all linear orderings embeddable into Rlex<Ï are either small or large. This fact sheds some light on the complicated structure of the linear ordering Rlex<Ï, and can be useful in applications to utility theory and preference modeling.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Alfio Giarlotta, Stephen Watson,