Kit Fine proved in [3] that the Interpolation Theorem failed in some standard quantified modal systems containning S5, and contradicted some results of K. A. Bowen, He wrote, 'Since Bowen’s proof of Robinson’s J...Kit Fine proved in [3] that the Interpolation Theorem failed in some standard quantified modal systems containning S5, and contradicted some results of K. A. Bowen, He wrote, 'Since Bowen’s proof of Robinson’s Joint Consistency Lemma （Theorem 10.1） is not given in detail, it is difficult to know where his error lies.' In fact, Bowen’s errors do not lie in the proofs themselves of the Joint Consistency Theorem （see Theorem 11.1 in [2] or Theorem 10.1 in [1]）, the Interpolation Theorem （see Theorem 11.2 in [2] or Theorem 10.2 in [1]）, and the Definability Theorem （see Theorem 11.5 in [2] or Theorem 10.3 in [1]）, but in the wrong theorems展开更多
文摘Kit Fine proved in [3] that the Interpolation Theorem failed in some standard quantified modal systems containning S5, and contradicted some results of K. A. Bowen, He wrote, 'Since Bowen’s proof of Robinson’s Joint Consistency Lemma （Theorem 10.1） is not given in detail, it is difficult to know where his error lies.' In fact, Bowen’s errors do not lie in the proofs themselves of the Joint Consistency Theorem （see Theorem 11.1 in [2] or Theorem 10.1 in [1]）, the Interpolation Theorem （see Theorem 11.2 in [2] or Theorem 10.2 in [1]）, and the Definability Theorem （see Theorem 11.5 in [2] or Theorem 10.3 in [1]）, but in the wrong theorems
