Titlebook: Logic: a Brief Course; Daniele Mundici Textbook 2012 Springer Milan 2012

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The Predicate Logic ,In this chapter, a bit more dense than the other ones, we describe a logic, denoted by ., and known as “predicate logic” or “elementary logic”, or also “first-order logic.” The syntax of . is perfectly tailored for the language of mathematics, which usually avoids clauses.

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G?del’s Compactness Theoremrefore we extend the notion of satisfiability as follows: . Let . be a (finite or infinite) set of clauses. Let . (.) denote the set of variables that occur in the clauses of .. Then an assignment α is . if the domain of α contains . (.). We say that α ., and write . if it satisfies each clause of . is . if no assignment satisfies it.

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Logic: a Brief Course978-88-470-2361-1Series ISSN 2038-5714 Series E-ISSN 2532-3318

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2038-5714 science and mathematics, is specifically designed for a first course in mathematical logic.A proof of G?del‘s completeness theorem and its main consequences is given using Robinson‘s completeness theorem and G?del‘s compactness theorem for propositionallogic. The reader will familiarize himself with

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Textbook 2012l logic.A proof of G?del‘s completeness theorem and its main consequences is given using Robinson‘s completeness theorem and G?del‘s compactness theorem for propositionallogic. The reader will familiarize himself with many basic ideas and artifacts of mathematical logic: a non-ambiguous syntax, logi