Mathematical LogicTaylor & 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. |
多く使われている語句
a₁ axiom of constructibility B₁ benign calculable Card(x cardinal closed formula consistency proof constructible continuum hypothesis corollary countable decision method defining axiom disjunction element elementarily equivalent elementary extension equality axioms equality theorem equivalent explicit definition expression numbers extension by definitions F is defined F is recursive finitary follows function F function or predicate function symbol functions and predicates H-index Hence Higman homomorphism hyperarithmetical identity axioms implies induction hypothesis infinite interpretation introduce isomorphism J-forces Lemma M-set n-ary function n-type natural numbers negation nonempty nonlogical axioms nonlogical symbols obtain ordinal partial functional predicate symbol prenex form problem provable prove quantifiers R-formula recursive function recursive partial functional recursively enumerable set relation replacing result special constants strongly undecidable structure subgroup subset suppose tautological consequence tautology theorem theory transfinite induction unary predicate valid variable-free variables Vy(y