Mathematical logic and foundations Model theory: basic notions Concept
Elementary substructure
Summary
An elementary substructure of a structure is a substructure that agrees with the big structure on first-order formulas. Each formula with parameters from the substructure has the same truth value in both. The big structure is then an elementary extension of the small one. Elementary substructures are the substructures that first-order logic cannot distinguish from the whole, even when it may name their elements.
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| Tag | 8WZF9SBP39 |
|---|---|
| URI | m2://8WZF9SBP39 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 03C07 |
| Specializes | Substructure |
| Changed | 2 November 2026 |
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