Some Basic Results of First-order Logic
We now introduce the basic notions of model and truth for first-order languages. Then we prove the completeness theorem, which shows the equivalence between the proof-theoretic notion ├ and the corresponding semantic notion. Following this we give a series of simple but basic results concerning first-order logic. Namely, we will discuss compactness, the elimination of operation symbols, extensions by definitions, Skolem functions, Herbrand’s theorem, and interpretations from one language to another. These results will be useful in discussing decidable and undecidable theories as well as in the model-theoretic portion of the book.
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