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Titlebook: Introduction to Mathematical Logic; Hans Hermes Textbook 1973 Springer-Verlag, Berlin/Heidelberg 1973 Logic.Mathematische Logik.calculus.m

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发表于 2025-3-21 18:16:56 | 显示全部楼层 |阅读模式
书目名称Introduction to Mathematical Logic
编辑Hans Hermes
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丛书名称Universitext
图书封面Titlebook: Introduction to Mathematical Logic; Hans Hermes Textbook 1973 Springer-Verlag, Berlin/Heidelberg 1973 Logic.Mathematische Logik.calculus.m
描述This book grew out of lectures. It is intended as an introduction to classical two-valued predicate logic. The restriction to classical logic is not meant to imply that this logic is intrinsically better than other, non-classical logics; however, classical logic is a good introduction to logic because of its simplicity, and a good basis for applications because it is the foundation of classical mathematics, and thus of the exact sciences which are based on it. The book is meant primarily for mathematics students who are already acquainted with some of the fundamental concepts of mathematics, such as that of a group. It should help the reader to see for himself the advantages of a formalisation. The step from the everyday language to a formalised language, which usually creates difficulties, is dis­ cussed and practised thoroughly. The analysis of the way in which basic mathematical structures are approached in mathematics leads in a natural way to the semantic notion of consequence. One of the substantial achievements of modern logic has been to show that the notion of consequence can be replaced by a provably equivalent notion of derivability which is defined by means of a calculu
出版日期Textbook 1973
关键词Logic; Mathematische Logik; calculus; mathematical logic; predicate logic; theorem
版次1
doihttps://doi.org/10.1007/978-3-642-87132-0
isbn_softcover978-3-540-05819-9
isbn_ebook978-3-642-87132-0Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag, Berlin/Heidelberg 1973
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Extensions of the Language, Normal Forms,In Chap. II, we built up the language of predicate logic on the basis of the junctors ⋀ and ┐ and the quantifier ⋀. Other junctors, such as V, →, ↔ (Chap. I, §6.2), and the quantifier V (Chap. I, §7.5) can be defined on this basis (see Chap. II, § 1.5; cf. also Chap. I, § 6, Exercise 5).
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The Semantics of Predicate Logic, on the basis of semantic ideas. The expressions of predicate logic correspond to the mathematical statements. In this chapter, we shall introduce the notion of consequence and the other semantic concepts which are necessary for its definition with the precision which is now possible.
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Introduction to Mathematical Logic978-3-642-87132-0Series ISSN 0172-5939 Series E-ISSN 2191-6675
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