Single Idea 10758

[catalogued under 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)


A Reaction

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