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Single Idea 13349

[from 'Intermediate Logic' by David Bostock, in 5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |= ]

Full Idea

If we write Γ |= φ, with one formula to the right, then the turnstile abbreviates 'entails'. For a sequent of the form Γ |= it can be read as 'is inconsistent'. For |= φ we read it as 'valid'.

Gist of Idea

Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid'

Source

David Bostock (Intermediate Logic [1997], 1.3)

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.13


Related Idea

Idea 13623 The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock]