Consequence Relations: An Introduction to the Lindenbaum-Tarski Method

The Mathematics of Metamathematics, An Algebraic Approach to Non-Classical Logics, and Theory of Logical Calculi created a niche in mathematical and philosophical logic. Citkin and Muravitsky's book discusses the problem of obtaining confirmation that a statement is a consequence of a set of statements and demonstrates that such confirmation does not exist in the structure under consideration. The concept of the Lindenbaum-Tarski algebra plays a key role in this problem, and the book includes helpful exercises to aid the reader's assimilation of the material. It is intended for advanced undergraduate and graduate students in mathematics and philosophy and can be used to teach special courses in logic with an emphasis on algebraic methods, for self-study, and as a reference work.

Format: Hardback
Length: 352 pages
Publication date: 29 July 2022
Publisher: Oxford University Press

The Mathematics of Metamathematics (1970) by Rasiowa and Sikorski, Rasiowa's An Algebraic Approach to Non-Classical Logics (1974), and Wójcicki's Theory of Logical Calculi (1988) all contributed to the development of a specialized field within mathematical and philosophical logic. This comprehensive exploration of the notion of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, fills this niche. Citkin and Muravitsky address two distinct problems. On the one hand, they consider the requirement of obtaining confirmation that a statement is a consequence of a set of statements. On the other hand, they address the challenge of demonstrating that such confirmation does not exist within the structure under consideration. The Lindenbaum-Tarski algebra assumes a pivotal role in addressing the second part of this problem, particularly when the considered consequence relation is contextualized within the realm of decidability. This role is intricately traced throughout the book, encompassing various formal objective languages. Additionally, the work includes helpful exercises designed to facilitate the reader's comprehension of the book's material. This book is intended for advanced undergraduate and graduate students in mathematics and philosophy. It serves as a valuable resource for teaching specialized courses in logic, with an emphasis on algebraic methods, for self-study, and as a reference work.

Weight: 708g
Dimension: 240 x 160 x 22 (mm)
ISBN-13: 9780192866417