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Syntactics of First-order Languages

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

Abstract

In this chapter we give the basic definitions and results concerning the syntax of first-order languages: terms, formulas, proofs, etc. As we proceed we shall also check the effectiveness of many of the notions, although at a later stage we shall just appeal to the weak Church’s thesis (see the comments preceding 3.3). This long section contains only very elementary facts, which will be used later mainly without citation. The basic definitions of syntactical notions occupy 10.1-10.18. The remainder of the chapter is concerned with elements of proof theory; this plays an important role in our discussion of decidable and undecidable theories in Part III, but will not be used in the discussion of model theory (Part IV).

Keywords

Atomic Formula Relation Symbol Operation Symbol Deduction Theorem Free Occurrence 
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Bibliography

  1. 1.
    Church, A. Introduction to Mathematical Logic, Vol. I. Princeton: Princeton Univ. Press (1956).MATHGoogle Scholar
  2. 2.
    Shoenfield, J. Mathematical Logic. Reading: Addison-Wesley (1967).MATHGoogle Scholar
  3. 3.
    Tarski, A. A simplified formalization of predicate logic with identity. Arch. f. Math. Logik u. Grundl., 7 (1965), 61–79.MathSciNetMATHCrossRefGoogle 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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