The canonical worlds are deductively closed implicational theories ordered by inclusion. A world forces an atom exactly when the atom belongs to that theory. The truth lemma says that a world forces an implicational formula exactly when the formula belongs to the theory.

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  1. Implicational fragment of intuitionistic propositional logic
  2. Intuitionistic propositional logic
  3. Propositional logic
  4. Mathematical logic
  5. Foundations of mathematics
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