Set Theory and Logic::

Author: Shen Enshao
Publisher:
Publish Date: 2003-04-01
Features: The logical part of this textbook is richer than that of similar materials, including the proof of the completeness theorem, compactness theorem, and the descending L-S theorem, which are typically introduced in graduate courses. One feature of this book is the use of Tableaux as a formalized deductive reasoning platform. This syntax-based proof system is more intuitive, simple, and easy to learn and use, and its ideas are widely applied in computer science and artificial intelligence. Another feature is a greater emphasis on the concepts, methods, and applications of semantics or model theory (such as the original idea of model checking). This book is suitable for students and teachers of computer science (undergraduate) and mathematics, as well as readers who aspire to further graduate studies. The book consists of two parts: a basic set theory and classical (first-order) logic. It serves as a high-standard textbook for computer science (undergraduate). The set theory part covers a scope similar to conventional textbooks, with differences in the way related content is presented and the depth of coverage. The adopted "non-standard" mode can be called an "axiomatic revision of classical set theory": it emphasizes axiomatic thinking and constructive techniques; provides a more in-depth treatment of "relational calculus" and "induction and recursion"; organically integrates several combinatorial and graph-theoretic principles and methods useful in computer science into the framework of set theory; and offers a more intuitive "panorama" of the world of set theory, without providing a complete introduction to axiomatic set theory.