Algebraic Set Theory PDF Download
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| Author | : André Joyal |
| Publisher | : Cambridge University Press |
| Total Pages | : 136 |
| Release | : 1995-09-14 |
| Genre | : Mathematics |
| ISBN | : 9780521558303 |
Download Algebraic Set Theory Book in PDF, ePub and Kindle
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.
| Author | : Norman T. Hamilton |
| Publisher | : Courier Dover Publications |
| Total Pages | : 289 |
| Release | : 2018-05-16 |
| Genre | : Mathematics |
| ISBN | : 0486830470 |
Download Set Theory: The Structure of Arithmetic Book in PDF, ePub and Kindle
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.
| Author | : Charles C Pinter |
| Publisher | : Courier Corporation |
| Total Pages | : 259 |
| Release | : 2014-07-23 |
| Genre | : Mathematics |
| ISBN | : 0486497089 |
Download A Book of Set Theory Book in PDF, ePub and Kindle
"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"--
| Author | : Robert R. Stoll |
| Publisher | : Courier Corporation |
| Total Pages | : 516 |
| Release | : 2012-05-23 |
| Genre | : Mathematics |
| ISBN | : 0486139646 |
Download Set Theory and Logic Book in PDF, ePub and Kindle
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.
| Author | : Joseph Breuer |
| Publisher | : Courier Corporation |
| Total Pages | : 130 |
| Release | : 2012-08-09 |
| Genre | : Mathematics |
| ISBN | : 0486154874 |
Download Introduction to the Theory of Sets Book in PDF, ePub and Kindle
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.
| Author | : Michael Potter |
| Publisher | : Clarendon Press |
| Total Pages | : 362 |
| Release | : 2004-01-15 |
| Genre | : Philosophy |
| ISBN | : 0191556432 |
Download Set Theory and its Philosophy Book in PDF, ePub and Kindle
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
| Author | : Jose Ferreiros |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 472 |
| Release | : 2001-11-01 |
| Genre | : Mathematics |
| ISBN | : 9783764357498 |
Download Labyrinth of Thought Book in PDF, ePub and Kindle
"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)
| Author | : Harry Pollard |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 1975-12-31 |
| Genre | : Algebraic number theory |
| ISBN | : 1614440093 |
Download The Theory of Algebraic Numbers: Second Edition Book in PDF, ePub and Kindle
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.
| Author | : John L. Bell |
| Publisher | : Courier Corporation |
| Total Pages | : 290 |
| Release | : 2008-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486462862 |
Download Toposes and Local Set Theories Book in PDF, ePub and Kindle
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
| Author | : Ilijas Farah |
| Publisher | : Springer Nature |
| Total Pages | : 517 |
| Release | : 2019-12-24 |
| Genre | : Mathematics |
| ISBN | : 3030270939 |
Download Combinatorial Set Theory of C*-algebras Book in PDF, ePub and Kindle
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.
