Linear O-minimal structures
Tóm tắt
A linearly ordered structure
$$\mathcal{M} = (M,< , \cdot \cdot \cdot )$$
is called o-minimal if every definable subset ofM is a finite union of points and intervals. Such an
$$\mathcal{M}$$
is aCF structure if, roughly said, every definable family of curves is locally a one-parameter family. We prove that if
$$\mathcal{M}$$
is aCF structure which expands an (interval in an) ordered group, then it is elementary equivalent to a reduct of an (interval in an) ordered vector space. Along the way we prove several quantifier-elimination results for expansions and reducts of ordered vector spaces.
Tài liệu tham khảo
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