Mathematical logic
著者
書誌事項
Mathematical logic
（Graduate texts in mathematics, 291）
Springer, c2021
3rd ed
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注記
Includes bibliographical references (p. 291-292) and index
内容説明・目次
内容説明
This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraisse's characterization of elementary equivalence, Lindstroem's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
目次
A.- I Introduction.- II Syntax of First-Order Languages.- III Semantics of First-Order Languages.- IV A Sequent Calculus.- V The Completeness Theorem.- VI The Loewenheim-Skolem and the Compactness Theorem.- VII The Scope of First-Order Logic.- VIII Syntactic Interpretations and Normal Forms.- B.- IX Extensions of First-Order Logic.- X Computability and Its Limitations.- XI Free Models and Logic Programming.- XII An Algebraic Characterization of Elementary Equivalence.- XIII Lindstroem's Theorems.- References.- List of Symbols.- Subject Index.
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