Mathematical Logic: A First Course
Suitable for advanced undergraduates and graduate students, this self-contained text will appeal to readers from diverse fields and varying backgrounds — including mathematics, philosophy, linguistics, computer science, and engineering. It features numerous exercises of varying levels of difficulty, many with solutions.
A survey of the propositional calculus is followed by chapters on first-order logic and first-order recursive arithmetic. An examination of the arithmetization of syntax follows, along with a review of the incompleteness theorems and other applications of the Liar Paradox. The text concludes with a study of second-order logic and an appendix on set theory that will prove valuable to students with little or no mathematical background.
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The Prepositional Calculus
1 Formation Rules for P
2 Formal Semantics of P
63 other sections not shown
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abbreviation appear applications arithmetic Assume axiom axiom schema called Chapter Clearly complete consistent construct contains countable course deduction theorem defined definition denoted elements equality equation exactly example Exercise exists finite first-order formal language formula function constant give given Godel number Hence holds implies individual constants individual variable Introduction Lemma mathematical means mechanics modus ponens n-place relation namely natural numbers notation Note obtain occurrence otherwise precisely predicate letters primitive recursive function primitive symbols problems proof properties proposition letter propositional calculus prove quantifier quantum mechanics reader relation replacing respectively rules satisfies schema second-order logic sentence sequence set of sentences Show structure substitution Suppose tautology term theorem schema tion true truth two-place universal valid VxP(x