| A necessary and sufficient condition for two realizations to be elementarily equivalent is that they admit ultrapowers that are isomorphic. |
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| Two realizations of the same language are said to be elementarily equivalent if they have the same set of true sentences. |
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| Two L-structures that are models of exactly the same sentences of L are said to be elementarily equivalent. |
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| One natural part of such a theory would be a purely structural necessary and sufficient condition for two structures to be elementarily equivalent. |
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| Kari's film was groundbreaking in that it was elementarily Icelandic and has been considered a contemporary classic with worldwide renown. |
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