Mathematical Logic - (Undergraduate Texts in Mathematics) 2nd Edition by H -D Ebbinghaus & J Flum & Wolfgang Thomas (Hardcover)
Similar Products
Products of same category from the store
All
Product info
<p/><br></br><p><b> Book Synopsis </b></p></br></br>What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe- matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godel's completeness theorem, which shows that the con- sequence relation coincides with formal provability: By means of a calcu- lus consisting of simple formal inference rules, one can obtain all conse- quences of a given axiom system (and in particular, imitate all mathemat- ical proofs). A short digression into model theory will help us to analyze the expres- sive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.<p/><br></br><p><b> From the Back Cover </b></p></br></br>The book starts with a thorough treatment of first-order logic and its role in the foundations of mathematics. It covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem Fraisse's characterization of elementary equivalence, Lindstrom's theorem on the maximality of first-order logic, and the fundamentals of logic programming.<p/><br></br><p><b> Review Quotes </b></p></br></br><br><p>"...the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level." - Journal of Symbolic Logic</p><br>
Price History
Price Archive shows prices from various stores, lets you see history and find the cheapest. There is no actual sale on the website. For all support, inquiry and suggestion messagescommunication@pricearchive.us