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elementarily equivalent
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(Definition)
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Definition The theory of a structure $\mathcal{M}{, }\theory(\mathcal{M}){,}$ is the set of all sentences of $\mathcal{L}$ that are true in $\mathcal{M}.$
Definition Structures $\mathcal{M}$ and $\mathcal{N}$ are elementarily equivalent, (in symbols: $\mathcal{M} \equiv \mathcal{N})$ if and only if $\theory(\mathcal{M}) = \theory(\mathcal{N})$
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"elementarily equivalent" is owned by CWoo. [ full author list (2) | owner history (2) ]
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Cross-references: sentences, language, first-order language, signature, structures
There are 164 references to this entry.
This is version 5 of elementarily equivalent, born on 2002-08-28, modified 2007-12-27.
Object id is 3388, canonical name is ElementarilyEquivalent.
Accessed 4601 times total.
Classification:
| AMS MSC: | 03C99 (Mathematical logic and foundations :: Model theory :: Miscellaneous) |
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Pending Errata and Addenda
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