Definitions of establish:

• verb:   set up or found
• verb:   use as a basis for; found on
• verb:   set up or lay the groundwork for

  Example: "Establish a new department"

• verb:   bring about

  Example: "The trompe l'oeil-illusion establishes depth"

• verb:   institute, enact, or establish
• verb:   build or establish something abstract
• verb:   establish the validity of something, as by an example, explanation or experiment
• verb:   place