Taylor & Francis, 2001/02/09 - 356 ページ
This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.
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adding apply assume benign calculable called cardinal choice choose Clearly closed formula complete Conclude condition consequence consider consistent constant constructible contains corollary defined definition designate distinct element elementary equality equivalent example existence explicit definition expression extension F is defined finite follows forces formal formula function F function symbol give given Hence holds implies individual induction hypothesis infinite interpretation introduce isomorphism language Lemma logical mapping means method natural numbers nonlogical axioms nonlogical symbols Note obtain occurrences otherwise partial functional predicate predicate symbol prenex form problem proof provable prove quantifiers recursive function recursively enumerable reducible relation replace represents result rule sequence Show stage structure subset substitution suffices suppose tautology theorem theorem theory transitive true truth undecidable valid variables write