Notes on proving of (strong) completeness theorem of L

The details of proving the completeness theorem of formula system L~*, which is given by Prof. Wang, are reviewed, and the proving of strong completeness about L~* is analyzed and revised. In addition, an equivalent description of representation theorem on strong negation operator is given, moreover, the generalized tautology on infinite valued logic based on different strong negation operators w.r.t. R_0-implication is studied, and a new partition based on fixed point of a strong negation is also obtained.