Single Idea 10238

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

Full Idea

Set theorists often point out that the set-theoretical hierarchy contains as many isomorphism types as possible; that is the point of the theory.

Gist of Idea

The set-theoretical hierarchy contains as many isomorphism types as possible

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 4.8)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.136


A Reaction

Hence there are a huge number of models for any theory, which are then reduced to the one we want at the level of isomorphism.