A Logical Foundation For Potentialist Set Theory

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A Logical Foundation for Potentialist Set Theory

Author : Sharon Berry
Publisher : Cambridge University Press
ISBN 13 : 1108998852
Total Pages : 250 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis A Logical Foundation for Potentialist Set Theory by : Sharon Berry

Download or read book A Logical Foundation for Potentialist Set Theory written by Sharon Berry and published by Cambridge University Press. This book was released on 2022-02-17 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist (as opposed to actualist) approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends her approach against a number of possible objections, and she shows how a notion of logical possibility that is useful in formulating Potentialist set theory connects in important ways with philosophy of language, metametaphysics and philosophy of science. Her book will appeal to readers with interests in the philosophy of set theory, modal logic, and the role of mathematics in the sciences.

Foundations of Set Theory

Author : Abraham Adolf Fraenkel
Publisher :
ISBN 13 :
Total Pages : 438 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Foundations of Set Theory by : Abraham Adolf Fraenkel

Download or read book Foundations of Set Theory written by Abraham Adolf Fraenkel and published by . This book was released on 1958 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Set Theory

Author : Kenneth Kunen
Publisher :
ISBN 13 : 9780444564023
Total Pages : 313 pages
Book Rating : 4.5/5 (64 download)

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Book Synopsis Set Theory by : Kenneth Kunen

Download or read book Set Theory written by Kenneth Kunen and published by . This book was released on 2006 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory" -- Provided by publisher.

The Joy of Sets

Author : Keith Devlin
Publisher : Springer Science & Business Media
ISBN 13 : 0387940944
Total Pages : 212 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis The Joy of Sets by : Keith Devlin

Download or read book The Joy of Sets written by Keith Devlin and published by Springer Science & Business Media. This book was released on 1994-06-24 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. 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.

Set Theory-An Operational Approach

Author : Luis E. Sanchis
Publisher : Routledge
ISBN 13 : 1351416839
Total Pages : 304 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Set Theory-An Operational Approach by : Luis E. Sanchis

Download or read book Set Theory-An Operational Approach written by Luis E. Sanchis and published by Routledge. This book was released on 2022-03-24 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a novel approach to set theory that is entirely operational. This approach avoids the existential axioms associated with traditional Zermelo-Fraenkel set theory, and provides both a foundation for set theory and a practical approach to learning the subject. It is written at the professional/graduate student level, and will be of interest to mathematical logicians, philosophers of mathematics and students of theoretical computer science.

Set Theory

Author : Kenneth Kunen
Publisher :
ISBN 13 : 9781848900509
Total Pages : 401 pages
Book Rating : 4.9/5 (5 download)

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Book Synopsis Set Theory by : Kenneth Kunen

Download or read book Set Theory written by Kenneth Kunen and published by . This book was released on 2011 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for readers who know elementary mathematical logic and axiomatic set theory, and who want to learn more about set theory. The primary focus of the book is on the independence proofs. Most famous among these is the independence of the Continuum Hypothesis (CH); that is, there are models of the axioms of set theory (ZFC) in which CH is true, and other models in which CH is false. More generally, cardinal exponentiation on the regular cardinals can consistently be anything not contradicting the classical theorems of Cantor and König. The basic methods for the independence proofs are the notion of constructibility, introduced by Gödel, and the method of forcing, introduced by Cohen. This book describes these methods in detail, verifi es the basic independence results for cardinal exponentiation, and also applies these methods to prove the independence of various mathematical questions in measure theory and general topology. Before the chapters on forcing, there is a fairly long chapter on "infi nitary combinatorics". This consists of just mathematical theorems (not independence results), but it stresses the areas of mathematics where set-theoretic topics (such as cardinal arithmetic) are relevant. There is, in fact, an interplay between infi nitary combinatorics and independence proofs. Infi nitary combinatorics suggests many set-theoretic questions that turn out to be independent of ZFC, but it also provides the basic tools used in forcing arguments. In particular, Martin's Axiom, which is one of the topics under infi nitary combinatorics, introduces many of the basic ingredients of forcing.

Foundations of Set Theory

Author : Abraham A. Fraenkel
Publisher :
ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.:/5 (299 download)

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Book Synopsis Foundations of Set Theory by : Abraham A. Fraenkel

Download or read book Foundations of Set Theory written by Abraham A. Fraenkel and published by . This book was released on 1973 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Set Theory

Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 0080954863
Total Pages : 365 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Set Theory by : Lev D. Beklemishev

Download or read book Set Theory written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set Theory

The Routledge Handbook of Modality

Author : Otávio Bueno
Publisher : Routledge
ISBN 13 : 1317585283
Total Pages : 432 pages
Book Rating : 4.3/5 (175 download)

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Book Synopsis The Routledge Handbook of Modality by : Otávio Bueno

Download or read book The Routledge Handbook of Modality written by Otávio Bueno and published by Routledge. This book was released on 2020-12-29 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modality - the question of what is possible and what is necessary - is a fundamental area of philosophy and philosophical research. The Routledge Handbook of Modality is an outstanding reference source to the key topics, problems and debates in this exciting subject and is the first collection of its kind. Comprising thirty-five chapters by a team of international contributors the Handbook is divided into seven clear parts: worlds and modality essentialism, ontological dependence, and modality modal anti-realism epistemology of modality modality in science modality in logic and mathematics modality in the history of philosophy. Within these sections the central issues, debates and problems are examined, including possible worlds, essentialism, counterfactuals, ontological dependence, modal fictionalism, deflationism, the integration challenge, conceivability, a priori knowledge, laws of nature, natural kinds, and logical necessity. The Routledge Handbook of Modality is essential reading for students and researchers in epistemology, metaphysics and philosophy of language. It will also be very useful for those in related fields in philosophy such as philosophy of mathematics, logic and philosophy of science.

Phenomenology, Logic, and the Philosophy of Mathematics

Author : Richard L. Tieszen
Publisher : Cambridge University Press
ISBN 13 : 0521837820
Total Pages : 369 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Phenomenology, Logic, and the Philosophy of Mathematics by : Richard L. Tieszen

Download or read book Phenomenology, Logic, and the Philosophy of Mathematics written by Richard L. Tieszen and published by Cambridge University Press. This book was released on 2005-06-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.

Set Theory: An Introduction

Author : Robert L. Vaught
Publisher : Birkhäuser
ISBN 13 : 9780817642563
Total Pages : 186 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Set Theory: An Introduction by : Robert L. Vaught

Download or read book Set Theory: An Introduction written by Robert L. Vaught and published by Birkhäuser. This book was released on 2001-08-28 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: By its nature, set theory does not depend on any previous mathematical knowl edge. Hence, an individual wanting to read this book can best find out if he is ready to do so by trying to read the first ten or twenty pages of Chapter 1. As a textbook, the book can serve for a course at the junior or senior level. If a course covers only some of the chapters, the author hopes that the student will read the rest himself in the next year or two. Set theory has always been a sub ject which people find pleasant to study at least partly by themselves. Chapters 1-7, or perhaps 1-8, present the core of the subject. (Chapter 8 is a short, easy discussion of the axiom of regularity). Even a hurried course should try to cover most of this core (of which more is said below). Chapter 9 presents the logic needed for a fully axiomatic set th~ory and especially for independence or consistency results. Chapter 10 gives von Neumann's proof of the relative consistency of the regularity axiom and three similar related results. Von Neumann's 'inner model' proof is easy to grasp and yet it prepares one for the famous and more difficult work of GOdel and Cohen, which are the main topics of any book or course in set theory at the next level.

Set Theory And Its Applications In Physics And Computing

Author : Yair Shapira
Publisher : World Scientific
ISBN 13 : 9811261792
Total Pages : 481 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Set Theory And Its Applications In Physics And Computing by : Yair Shapira

Download or read book Set Theory And Its Applications In Physics And Computing written by Yair Shapira and published by World Scientific. This book was released on 2022-06-24 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why learn set theory? This book provides the answer — it is interesting, and also useful! Taking a new approach and looking from a fresh perspective, the discussion flows in a friendly and transparent way, supplemented with a lot of examples and figures. This makes the theory easily comprehensible: the proofs get vivid and visual, enveloped with interesting applications for students in (applied) math, physics, and engineering. Given the theory and the applications, the book could serve as a textbook in four (undergraduate) math courses: Introduction to set theory and its application; Chaos theory and stability — a geometrical point of view; Functional analysis — Han-Banach theory; and Cryptography with quantum computing. It teaches set theory from the basics, including the axiom of choice, the well ordering theorem, and Zorn's lemma. Furthermore, it uses Cantor's set to introduce chaos theory from a geometrical point of view. Moreover, it introduces the binomial formula (and other related formulas), and uses them in quantum statistical mechanics. And finally, it uses Zorn's lemma in functional analysis, general relativity, and quantum mechanics. There are also practical applications in cryptography, error correction, quantum computing and programming.

Set Theory with an Introduction to Descriptive Set Theory

Author : Kuratowski
Publisher :
ISBN 13 :
Total Pages : 514 pages
Book Rating : 4.:/5 (131 download)

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Book Synopsis Set Theory with an Introduction to Descriptive Set Theory by : Kuratowski

Download or read book Set Theory with an Introduction to Descriptive Set Theory written by Kuratowski and published by . This book was released on 1976 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Set Theory with Applications

Author : Shwu-Yeng T. Lin
Publisher : Mancorp Publishing
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Set Theory with Applications by : Shwu-Yeng T. Lin

Download or read book Set Theory with Applications written by Shwu-Yeng T. Lin and published by Mancorp Publishing. This book was released on 1985 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Set Theory

Author : John L. Bell
Publisher : OUP Oxford
ISBN 13 : 0191620823
Total Pages : 216 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Set Theory by : John L. Bell

Download or read book Set Theory written by John L. Bell and published by OUP Oxford. This book was released on 2011-05-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.

Set Theory, Logic and Their Limitations

Author : Moshé Machover
Publisher :
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.:/5 (629 download)

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Book Synopsis Set Theory, Logic and Their Limitations by : Moshé Machover

Download or read book Set Theory, Logic and Their Limitations written by Moshé Machover and published by . This book was released on 1998 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reflections on the Foundations of Mathematics

Author : Stefania Centrone
Publisher : Springer Nature
ISBN 13 : 3030156559
Total Pages : 511 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Reflections on the Foundations of Mathematics by : Stefania Centrone

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.