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An Algebraic Introduction to Mathematical Logic / by D.W. Barnes, J.M. Mack
(Graduate Texts in Mathematics. ISSN:21975612 ; 22)
版 | 1st ed. 1975. |
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出版者 | (New York, NY : Springer New York : Imprint: Springer) |
出版年 | 1975 |
本文言語 | 英語 |
大きさ | IX, 123 p : online resource |
著者標目 | *Barnes, D.W author Mack, J.M author SpringerLink (Online service) |
件 名 | LCSH:Mathematical logic LCSH:Algebra FREE:Mathematical Logic and Foundations FREE:Algebra |
一般注記 | I Universal Algebra -- II Propositional Calculus -- III Properties of the Propositional Calculus -- IV Predicate Calculus -- V First-Order Mathematics -- VI Zermelo-Fraenkel Set Theory -- VII Ultraproducts -- VIII Non-Standard Models -- IX Turing Machines and Gödel Numbers -- X Hilbert’s Tenth Problem, Word Problems -- References and Further Reading -- Index of Notations This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a substantial course on abstract algebra. Consequently, our treatment of the subject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory HTTP:URL=https://doi.org/10.1007/978-1-4757-4489-7 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781475744897 |
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EB00234236 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA8.9-10.3 DC23:511.3 |
書誌ID | 4000107103 |
ISBN | 9781475744897 |
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