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FINITE-DIMENSIONAL ORDERED VECTOR SPACES WITH RIESZ INTERPOLATION AND EFFROS–SHEN’S UNIMODULARITY CONJECTURE
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 101 / Issue 2 / October 2016
- Published online by Cambridge University Press:
- 13 May 2016, pp. 277-287
- Print publication:
- October 2016
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- Article
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- You have access
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It is shown that, for any field
$\mathbb{F}\subseteq \mathbb{R}$, any ordered vector space structure of 
$\mathbb{F}^{n}$ with Riesz interpolation is given by an inductive limit of a sequence with finite stages 
$(\mathbb{F}^{n},\mathbb{F}_{\geq 0}^{n})$ (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 
$\mathbb{F}$ replaced by the integers, 
$\mathbb{Z}$. Indeed, it shows that although Effros and Shen’s conjecture is false, it is true after tensoring with 
$\mathbb{Q}$.
