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Titlebook: An Algebraic Introduction to Mathematical Logic; Donald W. Barnes,John M. Mack Textbook 1975 Springer Science+Business Media New York 1975

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發(fā)表于 2025-3-21 19:51:32 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱An Algebraic Introduction to Mathematical Logic
影響因子2023Donald W. Barnes,John M. Mack
視頻videohttp://file.papertrans.cn/155/154814/154814.mp4
發(fā)行地址Includes supplementary material:
學(xué)科分類Graduate Texts in Mathematics
圖書封面Titlebook: An Algebraic Introduction to Mathematical Logic;  Donald W. Barnes,John M. Mack Textbook 1975 Springer Science+Business Media New York 1975
影響因子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 of the sub-ject 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
Pindex Textbook 1975
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https://doi.org/10.1007/978-3-642-47386-9instruction of the list is applicable, producing a result to which exactly one instruction is applicable, until after a finite (but not necessarily bounded) number of steps, the process stops and a decision is announced.
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0072-5285 on 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 same978-1-4757-4491-0978-1-4757-4489-7Series ISSN 0072-5285 Series E-ISSN 2197-5612
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Propositional Calculus,odel of the system to be studied, and then conduct what is essentially a pure mathematical investigation of the properties of our model. Since this book is intended for mathematicians, the system we propose to study is not general logic but the logic used in mathematics. By this restriction, we achi
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Predicate Calculus,en collection of “primitive” statements is enlarged by combining statements. The Propositional Calculus does not analyse the original primitive statements. Our aim now is to construct a more complicated model of mathematical reasoning, which incorporates more of the ordinary features of this reasoni
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First-Order Mathematics,onstructed within the first-order predicate calculus will be called a first-order theory. By comparing a first-order theory with the informal theory on which it is modelled, we may gain insight into the influence of our logical system on our mathematics.
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