Download or read book Conceptions of Set and the Foundations of Mathematics written by Luca Incurvati and published by Cambridge University Press. This book was released on 2020-01-23 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Download or read book Abstract Set Theory written by Abraham Adolf Fraenkel and published by . This book was released on 1968 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory written by Douglas Cenzer and published by World Scientific. This book was released on 2020-04-04 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Foundations of Mathematics in the Theory of Sets written by John P. Mayberry and published by Cambridge University Press. This book was released on 2000 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Download or read book Sets for Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2003-01-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Download or read book Reflections on the Foundations of Mathematics written by Stefania Centrone and published by Springer Nature. This book was released on 2019-11-11 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.
Download or read book Set Theory and its Philosophy written by Michael Potter and published by Clarendon Press. This book was released on 2004-01-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Download or read book Problems and Theorems in Classical Set Theory written by Peter Komjath and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.
Download or read book Defending the Axioms written by Penelope Maddy and published by Oxford University Press. This book was released on 2011-01-27 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
Download or read book Set Theory and Logic written by Robert R. Stoll and published by Courier Corporation. This book was released on 2012-05-23 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Foundations of Mathematics written by Kenneth Kunen and published by . This book was released on 2009 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.
Download or read book Set Theory Arithmetic and Foundations of Mathematics written by Juliette Kennedy and published by Cambridge University Press. This book was released on 2011-09-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972-1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics.
Download or read book Homotopy Type Theory Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Axiomatic Set Theory written by Patrick Suppes and published by Courier Corporation. This book was released on 2012-05-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
Download or read book Labyrinth of Thought written by Jose Ferreiros and published by Springer Science & Business Media. This book was released on 2001-11-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: "José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
Download or read book Quine New Foundations and the Philosophy of Set Theory written by Sean Morris and published by Cambridge University Press. This book was released on 2018-12-13 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Download or read book Basic Set Theory written by Azriel Levy and published by Courier Corporation. This book was released on 2012-06-11 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.
