Tag: o-minimal

O-minimality and uniform finiteness

PatrickO-minimal structures / TeachingLeave a comment

Let ${\cal M}$ be an o-minimal expansion of a dense linear order $(M,\lt)$. The first big question about o-minimality is the following: is o-minimality an elementary property, that is, given ${\cal N} \equiv {\cal M}$, is ${\cal N}$ necessarily o-minimal? Lemma The following are equivalent: every ${\cal N} \equiv {\cal M}$ is o-minimal; for every…

O-minimal structures

PatrickO-minimal structures / TeachingLeave a comment

Let ${\cal M}$ be an expansion of a dense linear order $(M,\lt)$. We call ${\cal M}$ o-minimal if every definable subset of $M$ is a finite union of points and intervals. Examples (without details) By quantifier elimination, every dense linear order without endpoints is o-minimal. Let ${\cal V} = (V,\lt,+,(\lambda_k)_{k \in K})$ be an ordered…

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