The Foundations of Computability Theory

• Κύριος συγγραφέας: Robič, Borut (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015.
• Έκδοση: 1st ed. 2015.
• Θέματα: Computer science.; Computers.; Computer science > Mathematics.; Computer mathematics.; Computer Science.; Theory of Computation.; Mathematics of Computing.; Computational Mathematics and Numerical Analysis.

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theo...

Πίνακας περιεχομένων:

• Introduction
• The Foundational Crisis of Mathematics
• Formalism
• Hilbert’s Attempt at Recovery
• The Quest for a Formalization
• The Turing Machine
• The First Basic Results
• Incomputable Problems
• Methods of Proving the Incomputability
• Computation with External Help
• Degrees of Unsolvability
• The Turing Hierarchy of Unsolvability
• The Class D of Degrees of Unsolvability
• C.E. Degrees and the Priority Method
• The Arithmetical Hierarchy
• Further Reading
• App. A, Mathematical Background
• References
• Index.