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An Algebraic Introduction to Mathematical Logic (Graduate Texts in Mathematics, 22) 🔍
D.W. Barnes, Donald W. Barnes, John M. Mack Springer-Verlag New York, Softcover reprint of the original 1st ed. 1975, 2013
英语 [en] · PDF · 20.2MB · 2013 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/upload/zlib · Save
描述
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.
Erscheinungsdatum: 26.02.2013
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upload/bibliotik/D/Donald W. Barnes, John M. Mack - An Algebraic Introduction to Mathematical Logic (1975) [978-1-4757-4489-7].pdf
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lgli/Z:\Bibliotik_\19\D\Donald W. Barnes, John M. Mack - An Algebraic Introduction to Mathematical Logic (1975) [978-1-4757-4489-7].pdf
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lgrsnf/Z:\Bibliotik_\19\D\Donald W. Barnes, John M. Mack - An Algebraic Introduction to Mathematical Logic (1975) [978-1-4757-4489-7].pdf
备用文件名
nexusstc/Algebraic introduction to mathematical logic/e3bbd959084b5f3e3f1b65f0c49a8321.pdf
备用文件名
zlib/Mathematics/Barnes, D. W/Algebraic introduction to mathematical logic_5823080.pdf
备选作者
Barnes, D.W., Mack, J.M.
备选作者
P. R Halmos
备用出版商
Springer New York : Imprint : Springer
备用出版商
Springer London, Limited
备用出版商
Springer US
备用版本
Graduate texts in mathematics, 22, New York, NY, 1975
备用版本
Graduate texts in mathematics, v. 22, New York, 1975
备用版本
Place of publication not identified, 2013
备用版本
United States, United States of America
备用版本
Feb 26, 2013
元数据中的注释
lg2586120
元数据中的注释
producers:
Adobe Acrobat 9.2 Paper Capture Plug-in; modified using iText® 5.3.1 ©2000-2012 1T3XT BVBA (AGPL-version)
元数据中的注释
{"isbns":["1475744897","1475744919","9781475744897","9781475744910"],"publisher":"Springer"}
元数据中的注释
Source title: An Algebraic Introduction to Mathematical Logic (Graduate Texts in Mathematics)
备用描述
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 sub­ stantial course on abstract algebra. Consequently, our treatment ofthe sub­ ject is algebraic. Although we assurne 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 assurne 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 oflogic 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 co me only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory
备用描述
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 Goedel Numbers.- X Hilbert's Tenth Problem, Word Problems.- References and Further Reading.- Index of Notations.
开源日期
2020-07-26
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