Talk:Order embedding
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The model-theoretic perspective[edit]
I don't think it's true that an order embedding from A to B is the same thing as an isomorphism from A to an elementary substructure of B. Rather I think it should be "an isomorphism from A to a substructure of B".
For example, if B is a finite poset then its only elementary substructure is itself. Also if B is the set of all integers or all natural numbers, its only elementary substructure is itself. But obviously there are order-embeddings from posets to proper subsets of those B. Goedel Gang (talk) 20:28, 3 October 2023 (UTC)