Set Theory Logic And Their Limitations

This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.

Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.

Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.

From the Reviews: .,."He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know. ...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics." Philosophy and Phenomenological Research

This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.