more from John P. Burgess

### Single Idea 15411

#### [catalogued under 5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models]

Full Idea

In practice there is no need to consider any but mathematical models, models whose universes consist of mathematical objects, since every model is isomorphic to one of these.

Clarification

'isomorphic' means maps onto

Gist of Idea

We only need to study mathematical models, since all other models are isomorphic to these

Source

John P. Burgess (Philosophical Logic [2009], 1.8)

Book Reference

Burgess,John P.: 'Philosophical Logic' [Princeton 2009], p.10

A Reaction

The crucial link is the technique of Gödel Numbering, which can translate any verbal formula into numerical form. He adds that, because of the Löwenheim-Skolem theorem only subsets of the natural numbers need be considered.