General Theory of Undecidability
In previous chapters we have introduced several concepts related to the notion of undecidable theories (complete theories, 11.9; theories, 11.29; decidable and undecidable theories, 13.1; syntactical and weak syntactical definability, 14.1; recursive axiomatizability, 14.4; spectral representability, 14.22). Our purpose in this chapter is to establish various relationships known to exist between these notions and related ones. These general theorems will be applied in the next chapter, in which numerous examples of undecidable theories are given. We proceed in this chapter from the simpler concepts to the more complicated ones.
KeywordsRecursive Function Consistent Theory Finite Model Axiomatizable Theory Axiomatizable Extension
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