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Mathematical Logic

H.-D. Ebbinghaus, J. Flum, W. Thomas (Autoren)

Buch | Softcover

216 Seiten

1985 | 1984. 2nd Printing 1985 ed.
Springer-Verlag New York Inc.
9780387961705 (ISBN)

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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 Lindström'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.

Contents: Introduction.- Syntax of First-Order Languages.- Semantics of First-Order Languages.- A Sequent Calculus.- The Completeness Theorem.- The Löwenheim-Skolem Theorem and the Compactness Theorem.- The Scope of First-Order Logic.- Appendix. - Extensions of First-Order Logic.- Limitations of the Formal Method.- An Algebraic Characterization of Elementary Equivalence.- Characterizing First-Order Logic.- References.- Index of Notation.- Subject Index.

Erscheint lt. Verlag	15.7.1985
Reihe/Serie	Undergraduate Texts in Mathematics
Übersetzer	A. S. Ferebee
Zusatzinfo	1 Illustrations, black and white; IX, 216 p. 1 illus.
Verlagsort	New York, NY
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-13	9780387961705 / 9780387961705
Zustand	Neuware