Algebraic Set Theory
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Algebraic Set Theory
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Author : André Joyal
language : en
Publisher: Cambridge University Press
Release Date : 1995-09-14
Algebraic Set Theory written by André Joyal 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 1995-09-14 with Mathematics categories.
This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.
Combinatorial Set Theory Of C Algebras
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Author : Ilijas Farah
language : en
Publisher: Springer Nature
Release Date : 2019-12-24
Combinatorial Set Theory Of C Algebras written by Ilijas Farah and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-24 with Mathematics categories.
This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.
Set Theory The Structure Of Arithmetic
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Author : Norman T. Hamilton
language : en
Publisher: Courier Dover Publications
Release Date : 2018-05-16
Set Theory The Structure Of Arithmetic written by Norman T. Hamilton and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-16 with Mathematics categories.
This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 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.
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)
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"--
Elementary Number Theory
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Author : Ethan D. Bolker
language : en
Publisher: Courier Corporation
Release Date : 2012-06-14
Elementary Number Theory written by Ethan D. Bolker and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Mathematics categories.
This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and more.
Introduction To Set Theory
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Author : A. K. Sharma
language : en
Publisher: Discovery Publishing House
Release Date : 2010
Introduction To Set Theory written by A. K. Sharma and has been published by Discovery Publishing House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Set theory categories.
This book Introduction to Set Theory is very important in the field of modern algebra. It is very important to study this book to study modern mathematics. This book contain preliminary Notation, Sets, Subsets, Mapping Function and Relation. This book is useful to the students of under graduate, post graduate students and the candidate appearing in various competitions like pre Engineering/I.A.S/ P.C.S. etc. Contents: Preliminary Notation, Relations, Product or Composite of Mapping, Mapping or Functions
The Theory Of Algebraic Numbers Second Edition
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Author : Harry Pollard
language : en
Publisher: American Mathematical Soc.
Release Date : 1975-12-31
The Theory Of Algebraic Numbers Second Edition written by Harry Pollard 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 1975-12-31 with Mathematics categories.
This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
Model Theory And Algebraic Geometry
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Author : Elisabeth Bouscaren
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-17
Model Theory And Algebraic Geometry written by Elisabeth Bouscaren 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 1998-09-17 with Mathematics categories.
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.