Abstract
It is shown that, for any field F⊆R, any ordered vector space structure of Fn with Riesz interpolation is given by an inductive limit of a sequence with finite stages (Fn,Fn≥0) (where n does not change). This relates to a conjecture of Effros and Shen, since disproven, which is given by the same statement, except with F replaced by the integers, Z. Indeed, it shows that although Effros and Shen’s conjecture is false, it is true after tensoring with Q.
| Original language | English |
|---|---|
| Pages (from-to) | 277-287 |
| Number of pages | 11 |
| Journal | Journal of the Australian Mathematical Society |
| Volume | 101 |
| Issue number | 2 |
| Early online date | 13 May 2016 |
| DOIs | |
| Publication status | Published - Oct 2016 |
Keywords
- dimension groups
- Riesz interpolation
- ordered vector spaces
- unimodularity conjecture
- simplicial groups
- lattice-ordered groups
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