General Theory of Undecidability

  • J. Donald Monk
Part of the Graduate Texts in Mathematics book series (GTM, volume 37)


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.


Recursive Function Consistent Theory Finite Model Axiomatizable Theory Axiomatizable Extension 
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Copyright information

© Springer-Verlag Inc. 1976

Authors and Affiliations

  • J. Donald Monk
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA

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