Recursively Enumerable Sets

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


In this chapter we shall deal in some detail with the set Σ1 of relations (see 5.24). Such relations are called recursively enumerable for reasons which will shortly become clear. The study of recursively enumerable relations is one of the main branches of recursive function theory. They play a large role in logic. In fact, for most theories the set of Gödel numbers of theorems is recursively enumerable. Thus many of the concepts introduced in this section will have applications in our discussion of decidable and undecidable theories in Part III. Unless otherwise stated, the functions in this chapter are unary.


Productive Function Recursive Function Closure Property Partial Recursive Function Primitive Recursive Function 
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    Malcev, A. I. Algorithms and Recursive Functions. Groningen: Wolters-Noordhoff (1970).Google Scholar
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    Rogers, H. Theory of Recursive Functions and Effective Computability. New York: McGraw-Hill (1967).MATHGoogle Scholar
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    Smullyan, R. M. Theory of Formal Systems. Princeton: Princeton University Press (1961).MATHGoogle Scholar

Copyright information

© Springer-Verlag Inc. 1976

Authors and Affiliations

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

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