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| Author | : John P. Mayberry |
| Publisher | : Cambridge University Press |
| Total Pages | : 454 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780521770347 |
This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
| Author | : Luca Incurvati |
| Publisher | : Cambridge University Press |
| Total Pages | : 255 |
| Release | : 2020-01-23 |
| Genre | : History |
| ISBN | : 1108497829 |
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
| Author | : Abraham Adolf Fraenkel |
| Publisher | : |
| Total Pages | : 297 |
| Release | : 1968 |
| Genre | : |
| ISBN | : |
| Author | : Douglas Cenzer |
| Publisher | : World Scientific |
| Total Pages | : 222 |
| Release | : 2020-04-04 |
| Genre | : Mathematics |
| ISBN | : 9811201943 |
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.
| Author | : Stefania Centrone |
| Publisher | : Springer Nature |
| Total Pages | : 511 |
| Release | : 2019-11-11 |
| Genre | : Mathematics |
| ISBN | : 3030156559 |
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.
| Author | : Kenneth Kunen |
| Publisher | : |
| Total Pages | : 251 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 9781904987147 |
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.
| Author | : Charles C Pinter |
| Publisher | : Courier Corporation |
| Total Pages | : 259 |
| Release | : 2014-07-23 |
| Genre | : Mathematics |
| ISBN | : 0486497089 |
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
| Author | : Jose Ferreiros |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 472 |
| Release | : 2001-11-01 |
| Genre | : Mathematics |
| ISBN | : 9783764357498 |
"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)
| Author | : Patrick Suppes |
| Publisher | : Courier Corporation |
| Total Pages | : 290 |
| Release | : 2012-05-04 |
| Genre | : Mathematics |
| ISBN | : 0486136876 |
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.
| Author | : Robert R. Stoll |
| Publisher | : Courier Corporation |
| Total Pages | : 516 |
| Release | : 2012-05-23 |
| Genre | : Mathematics |
| ISBN | : 0486139646 |
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.
