Syntactics of First-order Languages
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).
KeywordsAtomic Formula Relation Symbol Operation Symbol Deduction Theorem Free Occurrence
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