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### Single Idea 10158

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

Full Idea

A structure is said to be a 'model' of an axiom system if each of its axioms is true in the structure (e.g. Euclidean or non-Euclidean geometry). 'Model theory' concerns which structures are models of a given language and axiom system.

Gist of Idea

A structure is a 'model' when the axioms are true. So which of the structures are models?

Source

Feferman / Feferman (Alfred Tarski: life and logic [2004], Int V)

Book Reference

Feferman,S/Feferman,A.B.: 'Alfred Tarski: life and logic' [CUP 2008], p.280

A Reaction

This strikes me as the most interesting aspect of mathematical logic, since it concerns the ways in which syntactic proof-systems actually connect with reality. Tarski is the central theoretician here, and his theory of truth is the key.