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Vdash

Represents a double vertical bar followed by a horizontal dash, commonly used in formal logic and mathematical proofs.

Overview

Serves as a specialized symbol in mathematical logic and proof theory, indicating a strong form of logical entailment or semantic consequence.

  • Frequently appears in formal logical arguments and mathematical demonstrations
  • Used to denote model-theoretic satisfaction or forcing relations
  • Common in advanced mathematics, particularly in set theory and mathematical logic
  • Often employed alongside other logical symbols to express complex logical relationships

Examples

Expressing logical consequence in formal logic notation.

p∧q⊩rp \land q \Vdash r 
p \land q \Vdash r

Showing semantic entailment in a modal logic formula.

□A⊩◊B\Box A \Vdash \Diamond B 
\Box A \Vdash \Diamond B

Representing model-theoretic forcing relation.

M⊩φ\mathcal{M} \Vdash \varphi 
\mathcal{M} \Vdash \varphi