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Single Idea 10758

[from 'First-order Logic, 2nd-order, Completeness' by Marcus Rossberg, in 5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms ]

Full Idea

A mathematical theory is 'categorical' if, and only if, all of its models are isomorphic. Such a theory then essentially has just one model, the standard one.

Gist of Idea

If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model

Source

Marcus Rossberg (First-order Logic, 2nd-order, Completeness [2004], §3)

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A Reaction

So the term 'categorical' is gradually replacing the much-used phrase 'up to isomorphism'.