### Single Idea 10899

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

Full Idea

A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true.

Gist of Idea

Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations

Source

José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5)

Book Reference

Zalabardo,José L.: 'Introduction to the Theory of Logic' [Westview 2000], p.102