Set Theory And Foundations Of Mathematics

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Conceptions Of Set And The Foundations Of Mathematics

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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.

Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory Second Edition

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Author : Douglas Cenzer
language : en
Publisher: World Scientific
Release Date : 2025-01-10

Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory Second Edition 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 2025-01-10 with Mathematics categories.

This book presents both axiomatic and descriptive set theory, targeting upper-level undergraduate and beginning graduate students. It aims to equip them for advanced studies in set theory, mathematical logic, and other mathematical fields, including analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory 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 through the text.This new edition includes additional topics on trees, ordinal functions, and sets, along with numerous new exercises. The presentation has been improved, and several typographical errors have been corrected.

Set Theory And Foundations Of Mathematics

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Author : DOUGLAS. PORTER CENZER (CHRISTOPHER. ZAPLETAL, JINDRICH.)
language : en
Publisher: World Scientific
Release Date : 2025

Set Theory And Foundations Of Mathematics written by DOUGLAS. PORTER CENZER (CHRISTOPHER. ZAPLETAL, JINDRICH.) and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with categories.

Reflections On The Foundations Of Mathematics

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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.

The Foundations Of Mathematics In The Theory Of Sets

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Author : John P. Mayberry
language : en
Publisher:
Release Date : 2000

The Foundations Of Mathematics In The Theory Of Sets written by John P. Mayberry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Electronic books categories.

This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.

Foundations Of Set Theory

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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.

Abstract Set Theory

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Author : Abraham Adolf Fraenkel
language : en
Publisher:
Release Date : 1968

Abstract Set Theory written by Abraham Adolf Fraenkel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.

Axiomatic Set Theory

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Author : Patrick Suppes
language : en
Publisher: Courier Corporation
Release Date : 1972-01-01

Axiomatic Set Theory written by Patrick Suppes and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-01-01 with Mathematics categories.

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.

Sets For Mathematics

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Author : F. William Lawvere
language : en
Publisher: Cambridge University Press
Release Date : 2003-01-27

Sets For Mathematics written by F. William Lawvere 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 2003-01-27 with Mathematics categories.

In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

Labyrinth Of Thought

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Author : Jose Ferreiros
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-01

Labyrinth Of Thought written by Jose Ferreiros and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-01 with Mathematics categories.

"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)