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In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

Gödel numbers. --- Logic, Symbolic and mathematical. --- Gödel, Kurt --- Gödel numbers --- Gödel's theorem. --- Logique symbolique er mathematique --- Gödel numbers --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Numbers, Gödel --- Number theory --- Gödel, Kurt. --- Gkentel, Kourt --- גדל --- Logique mathématique --- Gödel, Théorème de --- Incomplétude, Théorèmes d' --- Gödel's theorem --- Incompleteness theorems --- Logic, symbolic and mathematical --- Decidability (Mathematical logic) --- Gödel, Théorème de --- Gödel numbers. --- Gödel, Kurt Friedrich, --- Logique mathématique. --- Gödel, Théorème de. --- Incomplétude, Théorèmes d'. --- Arts and Humanities --- Philosophy --- Logique mathématique. --- Gödel, Théorème de. --- Incomplétude, Théorèmes d'. --- Gödel's theorem --- Gödel, Kurt