TeXipedia

pitchfork

Denotes the forcing relation in mathematical logic and set theory, particularly in the study of forcing methods.

Overview

Essential in advanced set theory and mathematical logic, this symbol represents a fundamental relationship between partial orders and generic extensions.

  • Commonly used in discussions of Cohen forcing and related techniques
  • Appears in research papers and texts on axiomatic set theory
  • Indicates a forcing relationship between conditions in a partial order and statements in the forcing language
  • Particularly relevant in independence proofs and consistency results in set theory

Examples

Expressing independence between random variables X and Y in probability theory.

X⋔YX \pitchfork Y 
X \pitchfork Y

Denoting model-theoretic independence in mathematical logic.

A⋔CBA \pitchfork_C B 
A \pitchfork_C B

Indicating independence of algebraic structures in abstract algebra.

G⋔H in KG \pitchfork H \text{ in } K 
G \pitchfork H \text{ in } K