was pursued by several logicians. The line of reasoning presented in Segerberg [1977] was the first attempt to prove the completeness of ⊢. Soon, Parikh came up with a proof, too. When early 1978 Segerberg found a flaw in his argument (which he repaired eventually), Parikh published what can be considered the first proof of the completeness of ⊢ in Parikh [1978]. Different proofs of completeness of ⊢ have been published since, e.g. Kozen and Parikh [1981].