关于MV-代数的逻辑性质

MV-代数是C．C．Chang为了提供Lukasiewicz和Tarski的多值逻辑系统的完备性定理的代数证明而发明的。它通过逻辑的观点，更进一步观察MV-代数的模型论性质。在本文中，我们研究了MV-代数的逻辑性质，得出形式化的MV-代数理论在子模、同态链的并之下有所保留；我们也证明了这个形式化的理论既不完备也不模型完备。

On the logical properties of MV-algebras

MV-algebras were invented by C. C. Chang1] in order to provide an algebraic proof of the completeness theorem of the infinite-valued logic of Lukasiewicz and Tarski. It seems appropriate to take a further look at the model properties of MV-algebras by a logical point of views. In this paper, we study the logical properties of MV-algebras. We proved that the formalized MV-algebras theory is preserved under submodels, homomorphisms, and unions of chains; we also proved that this formalized theory is neither complete nor model complete.