Mathematical Logic (Undergraduate Texts in Mathematics) （2 Reprint）

Ebbinghaus, H. D./ Flum, J./ Thomas, Wolfgang

Springer Nature（2012/12発売）

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製本 Paperback:紙装版/ペーパーバック版
言語 ENG
商品コード 9781475723571
DDC分類 511

Full Description

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.

Preface; Part ASemantics of first-Order Languages; 4. A Sequent Calculus; 5. The Completeness Theorem; 6. The Lowenheim-Skolem and the Compactness Theorem; 7. The Scope of First-Order Logic; 8. Syntactic Interpretations and Normal Forms; Part B: 9. Extensions of First-Order Logic; 10. Limitations of the Formal Method; 11. Free Models and Logic Programming; 12. An Algebraic Characterization of Elementary Equivalence; 13. Lindstroem's Theorems; References; Symbol Index; Subject Index