L_0^*-Lindenbaum代数的结构与性质

ON THE STRUCTURE AND PROPERTIES OF L_0~*-Lindenbaum ALGEBRA

讨论了L 系统的等价简化形式系统L 0 系统中Lindenbaum代数的结构与性质 .证明了 :(1)L 0 Linden baum代数是一个有界分配格 ;(2 )在L 0 系统中 ,(F(S) /≈ , )是一个含零元和单位元的Abel半群 ,这里对A ,B∈F(S) ,[A] [B]= ([A]→ [B]) .进一步 ,若设T是L 0 中的定理 ,A∈F(S) ,则 [A] [T]=[A],[A] [ T]=[ T].

For the structure and properties of L * 0 Lindenbaum algebra, the following conclusions are proved: (1)L * 0 Lindenbaum algebra can be made into a bounded distributive lattice; (2)the algebra (F(S)/≈,) is a Abel group with uniue element and zero element, where for A,B∈F(S), AB=(A→B). Moreover, if T is a theorem of L * 0, [T] is unite element and [T] is zero element.