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dashv

Represents a reversed turnstile symbol used in mathematical logic and set theory to denote semantic consequence or model relationships.

Overview

Commonly employed in formal logic and mathematical proofs to indicate semantic relationships between statements or models.

  • Often paired with its counterpart \vdash in logical notation
  • Used to express that a model satisfies a formula or theory
  • Appears frequently in proof theory and model theory discussions
  • Essential in formal semantics and mathematical foundations

Examples

Defining a relation that is not satisfied between sets.

ABA \dashv B
A \dashv B

Expressing non-derivability in formal logic.

PQRP \dashv Q \land R
P \dashv Q \land R

Showing a reverse turnstile relation in model theory.

Mφ\mathcal{M} \dashv \varphi
\mathcal{M} \dashv \varphi