Common
O-minimal theory
Type of infinite structure
O-minimal theory
In mathematical logic, and more specifically in model theory, an infinite structure ( M , < , … ) {\displaystyle (M,<,\dots )} that is totally ordered by < {\displaystyle <} is called an o-minimal structure if and only if every definable subset X ⊆ M {\displaystyle X\subseteq M} (with parameters taken from M {\displaystyle M} ) is a finite union of intervals and points. O-minimality can be regarded as a weak form of quantifier elimination. A structure M {\displaystyle M} is o-minimal if and only if every formula with one free variable and parameters in M {\displaystyle M} is equivalent to a quantifier-free formula involving only the ordering, also with parameters in...
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