One of the most beautiful sources of set theoretic wisdom is still hausdorffs set theory. A recent job change required me to come up to speed on set theory asap strange i know, but bang around in the industry long enough and youll be amazed at the stuff you have to learn, and this book was recommended. Instead of naive set theory a more honest title for the book would have been an outline of the elements of naive set theory. Naive set theory mathematical association of america. Which is to say, the book wont dig to the depths of formality or philosophy, it focuses on getting you productive with set theory. Though id imagine a lot of the shortness comes also from being naive set theory, rather than a fully rigorous treatment of axiomatic set theory. Naive set theory university series in undergraduate mathematics by halmos, paul r. This site is like a library, use search box in the widget to get ebook that you want.
Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It is roughly parallel in structure to halmoss classic naive set theory, though more topics have been added. Naive set theory download ebook pdf, epub, tuebl, mobi. I worked my way through halmos naive set theory, and did about of robert vaughts book. The standard book is paul halmos, naive set theory 1960. After working your way through this book youll be prepared to read more advanced and equality good texts. Unlike axiomatic set theories, which are defined using a formal logic, naive set theory is defined informally, in natural language. It then delves into contemporary set theory, covering such topics as the borel hierarchy and lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science. Publication date 1960 topics set theory, arithmetic publisher princeton, n. If you have similar goals, you can easily go through this book in a week if you think that learning set theory is worth your time.
Good books of naive set theory mathematics stack exchange. Halmos naive set theory is a classic and dense little book on axiomatic set theory, from a naive perspective. Apr 28, 2017 only a few exercises are designated as such since the book itself is an ongoing series of exercises with hints. Starting with the naive set theory of chapter i, we begin by asking the question what is a set. Its a clear, concise introduction to set theory, getting to the meat of it, without all the little asides and interesting things that distracts from learning the. It covers all these topics, and just a little more, but. Halmos is very skilled at presenting complicated ideas in terms that anyone can understand and enjoy. Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. These operations have been studied extensively since the birth of. However, formatting rules can vary widely between applications and fields of interest or study. Because of the informal method of presentation, the book is eminently suited for use. This book is read by people who are interested in reading books in category. The present treatment mightbest be described as axiomatic set theory from. Attempts to give a rlgorous answer lead naturally to the axioms of set theory introduced by zermelo and fraenkel, which is the system taken as basic in this book.
Click download or read online button to get naive set theory book now. Originally published by van nostrand in 1960, it was reprinted in the springerverlag undergraduate texts in mathematics series in 1974. Everyday low prices and free delivery on eligible orders. Every mathematician agrees that every mathematician must know some. One of the most beautiful sources of settheoretic wisdom is still hausdorffs set theory. Halmos naive set theory pdf beyond personal training. Halmos is very skilled at presenting complicated ideas in terms that anyone can understand and. I think the first half of irving kaplanskys book set theory and metric spaces fits what youre looking for. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. It describes the aspects of mathematical sets familiar in discrete mathematics for example venn diagrams and symbolic reasoning about their boolean. Set theory is everywhere in mathematics, and i personally appreciated shoring up my foundations. There we rely on everyones notion of set as a collection of objects or a container of objects. For its quality of exposition and coverage, this is the best place to start learning about set theory.
The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. This book has been written by paul r halmos, who has written books like lectures on ergodic theory,naive set theory,introduction to hilbert space and the theory of spectral multiplicity. Halmoss naive set theory is the type of book i look for most, when im interested in a topic outside my specialization, but would like to know it better to apply it to my research. Naive set theory by paul richard halmos, paperback. It is aimed at the beginning student of advanced mathematics. The book contains exercises in most chapters, in line with its super cial character of being an elementary set theory text, but no representation as. Buy naive set theory book online at low prices in india. Buy a cheap copy of naive set theory undergraduate texts in. This book is dedicated to prabir roy, louis mcauley.
These operations have been studied extensively since the birth of set theory. What are good booksother readings for elementary set theory. Also, there are only one or two exercises per chapter. It is aimed at the beginning student of advanced mathematics who wants to understand the settheoretic underpinnings of the mathematics he already knows or will learn soon. Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics.
Originally published by van nostrand in 1960, it was reprinted in the springerverlag undergraduate texts in mathematics series in 1974 while the title states that it is naive, which is usually taken to mean without axioms, the book does introduce all the axioms of zfc set theory. Arecent and highly readable addition to the literature, with an extensive and uptodate bibliography,isaxiomatic set theory bysuppes. It has been discovered that there is a number of operations on sets that bear a striking resemblance to the familiar operations of elementary algebra. Pdf naive set theory download full pdf book download. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. I later discovered endertons elements of set theory and i rec. Naive set theory by paul richard halmos, paperback barnes. This book is a very specialized but broadly useful introduction to set theory. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Every mathematician agrees that every mathematician must know some set theory. Naive set theory is a mathematics textbook by paul halmos providing an undergraduate introduction to set theory.
This book presents the classic relative consistency proofs in set theory that are obtained by the device of inner models. Much mathematics can be cleanly and axiomatically developed beginning with axiomatic set theory and then associating axiomatic rules to suitably defined sets and constructive relations. Halmos, 9780486814872, available at book depository with free delivery worldwide. The book is readable for its conciseness and clear explanation. An explicit ruling out of all conceivable inconsistencies paradoxes cannot be achieved for an axiomatic set theory anyway, due to godels second incompleteness theorem, so this does not at all hamper the utility of naive set theory as compared to axiomatic set theory in the simple contexts considered below. Paul halmoss book is the best introductory text to set theory. In set theory naive and axiomatic are contrasting words. The chapter also provides an overview on naive comprehension principle and the empty set.
Halmos was quite painful to work through, because there was little mathematical notation. As given in introduction to set theory of this course material, the concept of set is not defined rigorously in the naive set thoery which was originated by georg cantor. He the author uses the language and notation of ordinary informal mathematics to state the basic settheoretic facts which a beginning. Naive set theory is written in informal, conversational english, although the material is presented in a systematic and rigorous way. Naive set theory undergraduate texts in mathematics. Only a few exercises are designated as such since the book itself is an ongoing series of exercises with hints. A recent and highly readable addition to the literature, with an extensive and uptodate bibliography, is axiomatic set theory by suppes. The purpose of the book is to tell the beginning student of advanced mathematics the basic settheoretic facts.
The treatment covers the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters. Discover delightful childrens books with prime book box, a subscription that delivers new books every 1, 2, or 3 months new customers receive 15% off your. Search for library items search for lists search for contacts search for a library. Buy naive set theory by paul r halmos online at alibris. I dont particularly recommend set theory to armchair mathematicians.