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Single Idea 13636

[from 'Foundations without Foundationalism' by Stewart Shapiro, in 5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms ]

Full Idea

An axiomatization is 'categorical' if all its models are isomorphic to one another; ..hence it has 'essentially only one' interpretation [Veblen 1904].

Gist of Idea

An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1)

Book Reference

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.12