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### Single Idea 10162

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

Full Idea

In the late 1950s Tarski and Vaught defined and established basic properties of the relation of elementary equivalence between two structures, which holds when they make true exactly the same first-order sentences. This is fundamental to model theory.

Gist of Idea

Tarski and Vaught established the equivalence relations between first-order structures

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.282

A Reaction

This is isomorphism, which clarifies what a model is by giving identity conditions between two models. Note that it is 'first-order', and presumably founded on classical logic.