--- product_id: 8144000 title: "Set Theory and Logic (Dover Books on Mathematics)" price: "€ 53.59" currency: EUR in_stock: true reviews_count: 13 url: https://www.desertcart.pt/products/8144000-set-theory-and-logic-dover-books-on-mathematics store_origin: PT region: Portugal --- # Set Theory and Logic (Dover Books on Mathematics) **Price:** € 53.59 **Availability:** ✅ In Stock ## Quick Answers - **What is this?** Set Theory and Logic (Dover Books on Mathematics) - **How much does it cost?** € 53.59 with free shipping - **Is it available?** Yes, in stock and ready to ship - **Where can I buy it?** [www.desertcart.pt](https://www.desertcart.pt/products/8144000-set-theory-and-logic-dover-books-on-mathematics) ## Best For - Customers looking for quality international products ## Why This Product - Free international shipping included - Worldwide delivery with tracking - 15-day hassle-free returns ## Description 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 include: 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. Review: Broad, detailed, and beginner-friendly. - This is an ideal painless introduction to standard logic and set theory for anyone with a couple of years of undergraduate pure mathematics background. This 1963 book by Robert Roth Stoll is more than twice as big as the author's 1961 " Sets, Logic and Axiomatic Theories ", which it is an expansion of. The 1961 book was already very good, but this greatly expanded 1963 edition is much more comprehensive, and still very beginner-friendly, not one of those macho books which inflict the maximum pain on readers. Before proceeding to the more painful advanced logic and set theory books, it's probably a really good idea to first get relaxed and comfortable with this friendly introduction for a while. Instead of presenting formal logic first, as most of the advanced books do, Stoll starts with topics which are more familiar from general mathematics. Chapter 1 covers sets, relations, functions and order in a very elementary way. Chapter 2 (less elementary) presents natural numbers, cardinal numbers, ordinal numbers, and the axiom of choice. Chapter 3 presents rational and real numbers. The real numbers are constructed here using Cauchy sequences rather than Dedekind cuts. Then the logic starts in Chapter 4 with basic propositional and predicate calculus. Chapters 5, 6, 7 and 8 are concerned with the axiomatization of set theory and algebra. Finally Chapter 9 presents first-order languages and metamathematics, but not in too much depth. This lightweight introduction helps the reader to be comfortable with these concepts before optionally progressing to the more heavyweight model theory books. One consequence of presenting elementary set theorems before presenting set theory axioms is that some of Stoll's theorem's precede the axioms which they are based on. For example, theorems 4.4 and 4.5 on pages 91-93 use the countable axiom of choice, which is not introduced until pages 111-118 informally, and on page 302 formally. Interestingly, Stoll states on page 403 that David Hilbert believed that a metatheory "should belong to intuitive and informal mathematics". Stoll then states the following about Hilbert's view. "Further, its theorems [....] must be understood and the deductions must carry conviction. To help ensure the latter, all controversial principles of reasoning such as the axiom of choice must not be used." So this is a bit of meta-metamathematics by Hilbert. You don't read in many books about Hilbert's suspicions about the axiom of choice. One of the best things about this book is the presentation of a natural deduction logical calculus on page 183 in the tabular style of Suppes and Lemmon. This is, in my opinion, by far the best way to do propositional and predicate calculus rigorously and with minimum effort. There is some model theory and semantics in this book, but not too much. The set theory is standard ZF plus the axiom of choice. Not too much is said about interpretations, but just enough to prepare the reader for later studying model theory if they are that way inclined. Review: Great book - Nice book with a clear language and a bunch of examples and exercises in order for you to practice ## Technical Specifications | Specification | Value | |---------------|-------| | Best Sellers Rank | #286,344 in Books ( See Top 100 in Books ) #11 in Mathematical Set Theory #134 in Mathematical Logic #334 in Algebra & Trigonometry | | Customer Reviews | 4.6 out of 5 stars 113 Reviews | ## Images ![Set Theory and Logic (Dover Books on Mathematics) - Image 1](https://m.media-amazon.com/images/I/71WKMK0NsxL.jpg) ## Customer Reviews ### ⭐⭐⭐⭐⭐ Broad, detailed, and beginner-friendly. *by A***N on December 6, 2017* This is an ideal painless introduction to standard logic and set theory for anyone with a couple of years of undergraduate pure mathematics background. This 1963 book by Robert Roth Stoll is more than twice as big as the author's 1961 " Sets, Logic and Axiomatic Theories ", which it is an expansion of. The 1961 book was already very good, but this greatly expanded 1963 edition is much more comprehensive, and still very beginner-friendly, not one of those macho books which inflict the maximum pain on readers. Before proceeding to the more painful advanced logic and set theory books, it's probably a really good idea to first get relaxed and comfortable with this friendly introduction for a while. Instead of presenting formal logic first, as most of the advanced books do, Stoll starts with topics which are more familiar from general mathematics. Chapter 1 covers sets, relations, functions and order in a very elementary way. Chapter 2 (less elementary) presents natural numbers, cardinal numbers, ordinal numbers, and the axiom of choice. Chapter 3 presents rational and real numbers. The real numbers are constructed here using Cauchy sequences rather than Dedekind cuts. Then the logic starts in Chapter 4 with basic propositional and predicate calculus. Chapters 5, 6, 7 and 8 are concerned with the axiomatization of set theory and algebra. Finally Chapter 9 presents first-order languages and metamathematics, but not in too much depth. This lightweight introduction helps the reader to be comfortable with these concepts before optionally progressing to the more heavyweight model theory books. One consequence of presenting elementary set theorems before presenting set theory axioms is that some of Stoll's theorem's precede the axioms which they are based on. For example, theorems 4.4 and 4.5 on pages 91-93 use the countable axiom of choice, which is not introduced until pages 111-118 informally, and on page 302 formally. Interestingly, Stoll states on page 403 that David Hilbert believed that a metatheory "should belong to intuitive and informal mathematics". Stoll then states the following about Hilbert's view. "Further, its theorems [....] must be understood and the deductions must carry conviction. To help ensure the latter, all controversial principles of reasoning such as the axiom of choice must not be used." So this is a bit of meta-metamathematics by Hilbert. You don't read in many books about Hilbert's suspicions about the axiom of choice. One of the best things about this book is the presentation of a natural deduction logical calculus on page 183 in the tabular style of Suppes and Lemmon. This is, in my opinion, by far the best way to do propositional and predicate calculus rigorously and with minimum effort. There is some model theory and semantics in this book, but not too much. The set theory is standard ZF plus the axiom of choice. Not too much is said about interpretations, but just enough to prepare the reader for later studying model theory if they are that way inclined. ### ⭐⭐⭐⭐⭐ Great book *by R***O on October 26, 2024* Nice book with a clear language and a bunch of examples and exercises in order for you to practice ### ⭐⭐⭐⭐⭐ Very good coverage of set theory and logic. *by J***L on March 13, 2024* Very good coverage of set theory and logic. It's very readable, and also covers basic real analysis and the foundations of arithmetic. Ever wonder why a negative times a negative is a positive? i.e. why (-1)*(-1) === 1, this book answers this. ## Frequently Bought Together - Set Theory and Logic (Dover Books on Mathematics) - Number Theory (Dover Books on Mathematics) - Introduction to Graph Theory (Dover Books on Mathematics) --- ## Why Shop on Desertcart? - 🛒 **Trusted by 1.3+ Million Shoppers** — Serving international shoppers since 2016 - 🌍 **Shop Globally** — Access 737+ million products across 21 categories - 💰 **No Hidden Fees** — All customs, duties, and taxes included in the price - 🔄 **15-Day Free Returns** — Hassle-free returns (30 days for PRO members) - 🔒 **Secure Payments** — Trusted payment options with buyer protection - ⭐ **TrustPilot Rated 4.5/5** — Based on 8,000+ happy customer reviews **Shop now:** [https://www.desertcart.pt/products/8144000-set-theory-and-logic-dover-books-on-mathematics](https://www.desertcart.pt/products/8144000-set-theory-and-logic-dover-books-on-mathematics) --- *Product available on Desertcart Portugal* *Store origin: PT* *Last updated: 2026-09-04*