Research on General Theories of Decidability and Undecidability

• Main Authors: Yo-John Shi, 徐祐璋
• Other Authors: Hsing-Chien Tsai
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/87744892281898468249

碩士 === 國立中正大學 === 哲學所 === 97 === In order to discuss decidability/undecidability of theories, we first define first-order languages, structures, and theories in a language. Then we introduce interpretations and the related lemmas. We define and discuss some meta-logical properties, including essential undecidability, inseparability, and finite inseparability. However, we focus on finite inseparability and show that, by means of interpreting a finitely inseparable theory T0 to another theory T1, we have finite inseparability of T1. We introduce the universal language and then prove that the theory of the universal language is finitely inseparable. By interpretations of a theory to another, we show that many theories can be proved to be finitely inseparable and hence undecidable.