The Foundations Of Mathematics In The Theory Of Sets
DOWNLOAD
Download The Foundations Of Mathematics In The Theory Of Sets PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Foundations Of Mathematics In The Theory Of Sets book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Foundations Of Mathematics In The Theory Of Sets
DOWNLOAD
Author : John P. Mayberry
language : en
Publisher: Cambridge University Press
Release Date : 2000
The Foundations Of Mathematics In The Theory Of Sets written by John P. Mayberry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory
DOWNLOAD
Author : Douglas Cenzer
language : en
Publisher: World Scientific
Release Date : 2020-04-04
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory written by Douglas Cenzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-04 with Mathematics categories.
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.
Conceptions Of Set And The Foundations Of Mathematics
DOWNLOAD
Author : Luca Incurvati
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-23
Conceptions Of Set And The Foundations Of Mathematics written by Luca Incurvati and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with History categories.
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Foundations Of Set Theory
DOWNLOAD
Author : A.A. Fraenkel
language : en
Publisher: Elsevier
Release Date : 1973-12-01
Foundations Of Set Theory written by A.A. Fraenkel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-12-01 with Computers categories.
Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
The Foundations Of Mathematics
DOWNLOAD
Author : Ian Stewart
language : en
Publisher: Oxford University Press, USA
Release Date : 2015
The Foundations Of Mathematics written by Ian Stewart and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
Reflections On The Foundations Of Mathematics
DOWNLOAD
Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Reflections On The Foundations Of Mathematics written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
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.
Foundations Of Point Set Theory
DOWNLOAD
Author : Robert Lee Moore
language : en
Publisher: American Mathematical Soc.
Release Date : 1932-12-31
Foundations Of Point Set Theory written by Robert Lee Moore and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1932-12-31 with Mathematics categories.
The Foundations Of Mathematics
DOWNLOAD
Author : Kenneth Kunen
language : en
Publisher:
Release Date : 2009
The Foundations Of Mathematics written by Kenneth Kunen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
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.
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics
DOWNLOAD
Author : Douglas Cenzer
language : en
Publisher: World Scientific
Release Date : 2022-01-27
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics written by Douglas Cenzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-27 with Mathematics categories.
This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Gödel's Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy.
Set Theory And Foundations Of Mathematics
DOWNLOAD
Author : Douglas Cenzer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020
Set Theory And Foundations Of Mathematics written by Douglas Cenzer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
"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"--