1 - 9 of 9 Chapters
[In this section we introduce a basic kind of formal languages, first-order languages.]
[In this section we consider the interpretation of a first-order language, which consists in fixing a domain and a function that assigns a meaning of the appropriate sort for each individual constant, function constant and predicate constant.]
[In this section we introduce first-order theories, an elementary counterpart of mathematical axiomatic theories.]
[In this section we consider a noteworthy subclass of computable functions, the class of primitive recursive functions.]
[In this section we introduce some primitive recursive relations and functions which are meant to handle codes of finite sequences.]
[In this section we give a proof of Gödel’s First Incompleteness Theorem, based on the Traditional Fixed-Point Theorem.]
[In this section we consider Tarski’s two Undefinability Theorems, which establish in two different ways that the property of being a sentence true in N is not expressible in LPRA.]
[In this section we introduce languages that allow quantification not only on individual variables, but also on predicate variables.]
[In this section we introduce second-order theories, an extension of first-order theories to second-order logic.]
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