User:Thehalfone

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If $S$ is an infinite definable set of some structure (mathematical logic) and $A:=\{a_1,a_2,\ldots,a_n\}$ is any finite subset, then $A$ is definable via the formula (mathematical logic) $x=a_1 \lor x=a_2 \lor \ldots \lor x=a_n$ .

Similarly, any subset of $S$ which is cofinite, that is whose compliment is finite, is definable.

$S$ is said to be minimal iff these are the only definable subsets of $S$ .

A structure is said to be minimal iff its domain is a minimal set.

See also

Strong minimality

o-minimality

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