Let be a set, and let be an ultrafilter on , let be a formula of a given language , and let be any collection of structures
which is indexed by the set .
Denote by
the equivalence class of under , for any element of the product . Then the ultraproduct satisfies via a valuation in ,
be a set, and let 
be an ultrafilter on 
, let 
be a formula of a given language 
, and let 
be any collection of structures
which is indexed by the set 
.
Denote by ![[x]_U](/images/equations/LosTheorem/Inline8.svg)
the equivalence class of 
under 
, for any element 
of the product 
. Then the ultraproduct 
satisfies 
via a valuation ![s=[(x_i)_(i in I)]_U](/images/equations/LosTheorem/Inline15.svg)
in 
,
