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  • 数理逻辑(第2版)[平装]
  • 共3个商家     22.50元~40.95
  • 作者:艾宾浩斯(EbbinghausH.D.)(作者)
  • 出版社:世界图书出版公司;第1版(2008年5月1日)
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  • ISBN:9787506292276

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    《数理逻辑(第2版)》由世界图书出版公司出版。
    A short digression into model theory will help us to analyze the expressive 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 di~~culty 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.
    Godel‘s incompleteness theorems are presented in connection with several related results (such as Trahtenbrot’s theorem) which all exemplify the limitatious of machine-oriented proof methods. The notions of computability theory that are relevant to this discussion are given in detail.

    作者简介

    作者:(德国)艾宾浩斯(Ebbinghaus H.D.)

    目录

    Preface
    PART A
    I Introduction
    1.An Example from Group Theory
    2.An Example from the Theory of Equivalence Relations
    3.A Preliminary Analysis
    4.Preview
    II Syntax of First-Order Languages
    1.Alphabets
    2.The Alphabet of a First-Order Language
    3.Terms and Formulas in First-Order Languages
    4.Induction in the Calculus of Terms and in the Calculus of Formulas
    5.Free Variables and Sentences
    III Semantics of First-Order Languages
    1.Structures and Interpretations
    2.Standardization of Connectives
    3.The Satisfaction Relation
    4.The Consequence Relation
    5.Two Lemmas on the Satisfaction Relation
    ……