Intuitive Axiomatic Set Theory
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Intuitive Axiomatic Set Theory
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Author : José L Garciá
language : en
Publisher: CRC Press
Release Date : 2024-04-04
Intuitive Axiomatic Set Theory written by José L Garciá and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-04 with Mathematics categories.
Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable. The book has two parts. The first one presents, from the sole intuition of "collection" and "object", the axiomatic ZFC-theory. Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes. The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic. The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.
Intuitive Axiomatic Set Theory
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Author : José Luis García
language : en
Publisher:
Release Date : 2024
Intuitive Axiomatic Set Theory written by José Luis García and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with categories.
"Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory and thus knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible, but also valuable"--
Intuitive Axiomatic Set Theory
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Author : José L Garciá
language : en
Publisher: CRC Press
Release Date : 2024-04-04
Intuitive Axiomatic Set Theory written by José L Garciá and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-04 with Mathematics categories.
Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable. The book has two parts. The first one presents, from the sole intuition of "collection" and "object", the axiomatic ZFC-theory. Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes. The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic. The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.
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.
Set Theory An Intuitive Approach
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Author : Shwu Yeng T. Lin
language : en
Publisher:
Release Date : 1974
Set Theory An Intuitive Approach written by Shwu Yeng T. Lin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Teoria de grupos categories.
A Book Of Set Theory
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Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2014-07-23
A Book Of Set Theory written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Mathematics categories.
"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"--
Introduction To The Theory Of Sets
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Author : Joseph Breuer
language : en
Publisher: Courier Corporation
Release Date : 2012-08-09
Introduction To The Theory Of Sets written by Joseph Breuer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-09 with Mathematics categories.
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Set Theory With Applications
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Author : Shwu-Yeng T. Lin
language : en
Publisher: Mancorp Publishing
Release Date : 1985
Set Theory With Applications written by Shwu-Yeng T. Lin and has been published by Mancorp Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Axiomatic Set Theory
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Author : Patrick Suppes
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04
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 2012-05-04 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.
Set Theory And Logic
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Author : Robert R. Stoll
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Set Theory And Logic written by Robert R. Stoll and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
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.