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Full Idea
The syntactic turnstile |- φ means 'There is a proof of φ' (in the system currently being considered). Another way of saying the same thing is 'φ is a theorem'.
Gist of Idea
The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem'
Source
David Bostock (Intermediate Logic [1997], 5.1)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.192
Related Ideas
Idea 13348 It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock]
Idea 13349 Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock]
| 11148 | Deduction is when we suppose one thing, and another necessarily follows [Aristotle] |
| 18277 | If q implies p, that is justified by q and p, not by some 'laws' of inference [Wittgenstein] |
| 13623 | The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock] |
| 13722 | A 'theorem' is an axiom, or the last line of a legitimate proof [Sider] |
| 22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter] |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| 18808 | Normal deduction presupposes the Cut Law [Rumfitt] |