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Single Idea 10884

[filed under theme 5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms ]

Full Idea

If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'.

Gist of Idea

A theory is 'categorical' if it has just one model up to isomorphism

Source

Leon Horsten (Philosophy of Mathematics [2007], §5.2)

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.23

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The 4 ideas from 'Philosophy of Mathematics'

10881

The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]

10882

Predicative definitions only refer to entities outside the defined collection [Horsten]

10884

A theory is 'categorical' if it has just one model up to isomorphism [Horsten]

10885

Computer proofs don't provide explanations [Horsten]