Kategoria BISAC: Mathematics >> Logic

This monograph covers the recent major advances in various areas of set theory.

From the reviews:

"One of the classical textbooks and reference books in set theory....The present 'Third Millennium' edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS

Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3.

This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e....

The author investigates proofs of correctness of realistic security protocols in a formal, intuitive setting. The protocols examined include Kerberos versions, smartcard protocols, non-repudiation protocols, and certified email protocols. The method of analysis turns out to be both powerful and flexible. This research advances significant extensions to the method of analysis, while the findings on the protocols analysed are novel and illuminating.

Jean-Pierre Jouannaud has deeply influenced, and is still influencing, research in Informatics, through the many important results he has produced in various research fields and through the generations of scholars he has educated. He has played a leading role in field of rewriting and its technology, advancing the research areas of unification, rewriting and completion modulo, conditional rewriting, termination proofs, modular properties, and automated proofs by induction in rewrite theories. Following his strong interest for algebraic specification languages and their efficient...

This textbook guides students through algebraic specification and verification of distributed systems, and some of the most prominent formal verification techniques. The author employs CRL as the vehicle, a language developed to combine process algebra and abstract data types. The book evolved from introductory courses on protocol verification taught to undergraduate and graduate students of computer science, and the text is supported throughout with examples and exercises. Full solutions are provided in an appendix, while exercise sheets, lab exercises, example specifications and lecturer...

The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet. The foundational debate is presented with all its brilliant contributions and its shortcomings, its new ideas and its misunderstandings.