Mathematical logic
著者
書誌事項
Mathematical logic
（Undergraduate texts in mathematics）
Springer-Verlag, c1984
- : us
- : gw
- タイトル別名
-
Einführung in die mathematisch Logik
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注記
Bibliography: p. [209]-210
Includes indexes
内容説明・目次
内容説明
This careful, self-contained introduction to first-order logic includes an exposition of certain topics not usually found in introductory texts (such as Trachtenbrot's undecidability theorem, Fraisse's characterization of elementary equivalence, and Lindstrom's theorem on the maximality of first-order logic). The presentation is detailed and systematic without being long-winded or tedious. The role of first-order logic in the foundations of mathematics is worked out clearly, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. Many exercises accompany the text.
目次
- Syntax of first-order languages
- semantics of first-order languages
- a sequent calculus
- the completeness theorem
- the Lowenheim-Skolem theorem and the compactness theorem
- the scope of first-order logic
- appendix
- extension of first-order logic
- limitations of the formal method
- an algebraic characterization of elementary equivalence
- characterizing first-order logic.
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