Set Theory and Logic

by Robert Roth Stoll

Set Theory and Logic is the result of a course of lectures for advanced undergraduates, developed at Oberlin College for the purpose of introducing students to the conceptual foundations of mathematics. Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms. One of the most complex and essential of modern mathematical innovations, the theory of sets (crucial to quantum mechanics and other sciences), is introduced in a most careful concept manner, aiming for the maximum in clarity and stimulation for further study in set logic.
Contents Sets and Relations — Cantor's concept of a set, etc.
Natural Number Sequence — Zorn's Lemma, etc.
Extension of Natural Numbers to Real Numbers
Logic — the Statement and Predicate Calculus, etc.
Informal Axiomatic Mathematics
Boolean AlgebraInformal Axiomatic Set TheorySeveral Algebraic Theories — Rings, Integral Domains, Fields, etc.
First-Order Theories — Metamathematics, etc.
Symbolic logic does not figure significantly until the final chapter. The main theme of the book is mathematics as a system seen through the elaboration of real numbers; set theory and logic are seen s efficient tools in constructing axioms necessary to the system.
Mathematics students at the undergraduate level, and those who seek a rigorous but not unnecessarily technical introduction to mathematical concepts, will welcome the return to print of this most lucid work.
"Professor Stoll . . . has given us one of the best introductory texts we have seen." — Cosmos .
"In the reviewer's opinion, this is an excellent book, and in addition to its use as a textbook (it contains a wealth of exercises and examples) can be recommended to all who wish an introduction to mathematical logic less technical than standard treatises (to which it can also serve as preliminary reading)." — Mathematical Reviews.

Genres: Mathematics, Logic, Science, Nonfiction, Philosophy, Textbooks

512 pages, Paperback

First published January 1, 1968

Reviews

[Miguel Ramírez · Rating 4 out of 5]

This is the most didactic introduction to Set Theory I have found in print. All definitions have attached non-trivial and interesting examples. The exercises are well-organized and chosen with care. It often uses terminology that is not commonly used in the 2020s as it was in the 1970s (the book's latest edition is from 1979), but these issues are straightforward to navigate.

[Dave Peticolas · Rating 3 out of 5]

A great introdution to, well, set theory and logic.

[Max · Rating 5 out of 5]

Excellent, well-structured introduction to formal logic and set theory.