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28 year-old Painting Investments Worker Truman from Regina, usually spends time with pastimes for instance interior design, property developers in new launch ec Singapore and writing. Last month just traveled to City of the Renaissance. In model theory, a branch of mathematical logic, and in algebra, the reduced product is a construction that generalizes both direct product and ultraproduct.

Let {S_i | i ∈ I} be a family of structures of the same signature σ indexed by a set I, and let U be a filter on I. The domain of the reduced product is the quotient of the Cartesian product

$\prod _{i\in I}{S}_i$

by a certain equivalence relation ~: two elements (a_i) and (b_i) of the Cartesian product are equivalent if

$\{i\in I:a_i=b_i\}\in U$

If U only contains I as an element, the equivalence relation is trivial, and the reduced product is just the original Cartesian product. If U is an ultrafilter, the reduced product is an ultraproduct.

Operations from σ are interpreted on the reduced product by applying the operation pointwise. Relations are interpreted by

$R((a_i^1)/\sim ,\dots ,(a_i^n)/\sim )⟺\{i\in I\mid R^{S_i}(a_i^1,\dots ,a_i^n)\}\in U.$

For example, if each structure is a vector space, then the reduced product is a vector space with addition defined as (a + b)_i = a_i + b_i and multiplication by a scalar c as (ca)_i = c a_i.

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534, Chapter 6.

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