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 Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics)

Science & Math

Thomas, Wolfgang

Flum, J.

Ebbinghaus, H.D.

Mathematics

Springer

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.

Mathematical Logic (Undergraduate Texts in Mathematics)

Thomas, W.

This book is a state-of-the-art introduction into both algorithmic techniques for fixed-parameter tractability and the structural theory of parameterized complexity classes. It presents detailed proofs of recent advanced results that have not appeared in book form before and replaces the earlier publication "Parameterized Complexity" by Downey and Fellows as the definitive book on this subject. The book will interest computer scientists, mathematicians and graduate students engaged with algorithms and problem complexity.

Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)

Computers & Technology

Grohe, M.

Computer Science

Was ist ein mathematischer Beweis? Wie lassen sich Beweise rechtfertigen? Gibt es Grenzen der Beweisbarkeit? Ist die Mathematik widerspruchsfrei? Kann man das Auffinden mathematischer Beweise Computern übertragen? Erst im 20. Jahrhundert ist es der mathematischen Logik gelungen, weitreichende Antworten auf diese Fragen zu geben: Im vorliegenden Werk werden die Ergebnisse systematisch zusammengestellt; im Mittelpunkt steht dabei die Logik erster Stufe. Die Lektüre setzt 'außer einer gewissen Vertrautheit mit der mathematischen Denkweise' keine spezifischen Kenntnisse voraus. In der vorliegenden 5. Auflage finden sich erstmals Lösungsskizzen zu den Aufgaben.

Einführung in die Mathematische Logik (Sav Mathematik) (German Edition)

Spektrum Akademischer Verlag

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