### Single Idea 10477

#### [catalogued under 5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=]

Full Idea

If every structure which is a model of a set of sentences T is also a model of one of its sentences φ, then this is known as the model-theoretic consequence relation, and is written T |= φ. Not to be confused with |= meaning 'satisfies'.

Gist of Idea

|= in model-theory means 'logical consequence' - it holds in all models

Source

Wilfrid Hodges (Model Theory [2005], 3)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.7

A Reaction

See also Idea 10474, which gives the other meaning of |=, as 'satisfies'. The symbol is ALSO used in propositional logical, to mean 'tautologically implies'! Sort your act out, logicians.

Related Idea

Idea 10474
|= should be read as 'is a model for' or 'satisfies' **[Hodges,W]**