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First-order Model Theory (6168 words) |
 | Elementary equivalence is an equivalence relation on the class of all L-structures. |
| We say that A is an elementary substructure of B, and B is an elementary extension of A, if A is a substructure of B and the inclusion map is an elementary embedding. |
| Then there are an elementary extension D of B and an elementary embedding e of C into D such that (i) for each element a of A, e(a) = a, and (ii) if c is an element of C but not of A, then e(c) is not in B. |
| PlanetMath: (2166 words) |
| elementary abelian (in elementary abelian group) owned by yark |
| elementary extension (in elementary embedding) owned by Henry |
| elementary symmetric polynomial in terms of power sums owned by rspuzio |
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