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- n. A quotient of the direct product of a family of structures
ÅoÅ's theorem describes what sentences are true in an ultraproduct.
If C is a power of A then this ultraproduct is called an ultrapower of A, and it is sometimes written U-prod A.
This is indeed an equivalence relation on the domain of C, and the resulting reduced product is called an ultraproduct of the factors of
We refer the reader to the entry on first-order model theory for the notions of direct product (called product there) and ultraproduct.
As an example, the notions of quotient, direct product, ultraproduct are defined and examined.