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Single Idea 17930

[filed under theme 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation ]

Full Idea

A set of axioms is said to be 'categorical' if all models of the axioms in question are isomorphic.

Gist of Idea

Axioms are 'categorical' if all of their models are isomorphic

Source

Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2)

Book Ref

Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.25

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A Reaction

The best example is the Peano Axioms, which are 'true up to isomorphism'. Set theory axioms are only 'quasi-isomorphic'.