Post Completeness in Modal Logic

@article{Segerberg1972PostCI,
  title={Post Completeness in Modal Logic},
  author={Krister Segerberg},
  journal={J. Symb. Log.},
  year={1972},
  volume={37},
  pages={711-715}
}
Let ⊥, →, and □ be primitive, and let us have a countable supply of propositional letters. By a ( modal) logic we understand a proper subset of the set of all formulas containing every tautology and being closed under modus ponens and substitution. A logic is regular if it contains every instance of □A ∧ □B ↔ □(A ∧ B) and is closed under the rule A regular logic is normal if it contains □⊤. The smallest regular logic we denote by C (the same as Lemmon's C2 ), the smallest normal one by K . If L… CONTINUE READING
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