more from Wilfrid Hodges

### Single Idea 10478

#### [catalogued under 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic]

Full Idea

In first-order languages the completeness theorem tells us that T |= φ holds if and only if there is a proof of φ from T (T |- φ). Since the two symbols express the same relationship, theorist often just use |- (but only for first-order!).

Gist of Idea

Since first-order languages are complete, |= and |- have the same meaning

Source

Wilfrid Hodges (Model Theory [2005], 3)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.8

A Reaction

[actually no spaces in the symbols] If you are going to study this kind of theory of logic, the first thing you need to do is sort out these symbols, which isn't easy!