Alexei Muravitsky – författare
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The publication of Rasiowa and Sikorski's The Mathematics of Metamathematics (1970), Rasiowa's An Algebraic Approach to Non-Classical Logics (1974), and Wójcicki's Theory of Logical Calculi (1988) created a niche in the field of mathematical and philosophical logic. This in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, fills this niche. Citkin and Muravitsky consider the problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites, on the one hand, and the problem of demonstrating that such confirmation does not exist in the structure under consideration, on the other hand. For the second part of this problem, the concept of the Lindenbaum-Tarski algebra plays a key role, which becomes even more important when the considered consequence relation is placed in the context of decidability. This role is traced in the book for various formal objective languages. The work also includes helpful exercises to aid the reader's assimilation of the book's material. Intended for advanced undergraduate and graduate students in mathematics and philosophy, this book can be used to teach special courses in logic with an emphasis on algebraic methods, for self-study, and also as a reference work.
Legacy of A.V. Kuznetsov in Logic, Algebra and the Foundations of Mathematics
Inbunden, Engelska, 2026
2 133 kr
Kommande
This book is dedicated to the 100th anniversary of the birth of A. V. Kuznetsov, who was born in 1926 and whose achievements laid new paths for the development of many branches of non-classical logic in the 1950s-1980s, influencing many researchers in the field to this day. Kuznetsov's formal education lasted only until the sixth grade of school, so he can be considered self-taught; however, he became one of the most prominent figures in the field of mathematical logic in the former USSR. While obtaining new results in various areas of mathematical logic, sometimes unrelated to each other, as well as in the related areas of universal algebra, he used to be quite careless about their publication. The approach taken in this book is threefold. it places Kuznetsov's well-known results in a historical perspective; second - some lesser-known results of Kuznetsov are brought to the broader English-reading audience, not only experts in the field. Third, new results that clearly bear the influence of Kuznetsov are presented.