On the metatheory of classical propositional logic

• Main Authors: Tzu- Keng Fu, 傅子耕
• Other Authors: 李國偉
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/86601431532012659596

碩士 === 國立中正大學 === 哲學所 === 93 === The topic of this thesis is ``On the metatheoy of classical propositional logic". I prove that the metatheory of propositional logic is undecidable, and using one of Turing's result to prove it is also non-axiomatizable. This thesis offers three arguments, the first one is to prove $Th(langle vdash angle)$ is decidable, the second one is to prove $Th(langle vdash angle)$ is decidable, and the third one is to prove $Th(PROP)$ is undecidable. From these three proofs, we get the main result of this thesis, and these three proofs can also be three examples for three methods of proving the decidability problems separately. Especially emphasizing, when doing the first two proofs, I refer to some methods in model theory, to use these classical ways, we find it is clear and easy to finish these two proofs. Besides, when doing the third proof, I follow the method that Ian Mason offers in his paper[7]. Although this method can help us derive the result that we want effectively, many details is not clear such that the readers can not realize easily. The other purpose is to make details well-done.