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Set Theory The Structure Of Arithmetic
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Book Synopsis Set Theory: The Structure of Arithmetic by : Norman T. Hamilton
Download or read book Set Theory: The Structure of Arithmetic written by Norman T. Hamilton and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Set Theory and the Structure of Arithmetic by : Norman Hamilton
Download or read book Set Theory and the Structure of Arithmetic written by Norman Hamilton and published by . This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Set Theory and its Philosophy by : Michael Potter
Download or read book Set Theory and its Philosophy written by Michael Potter and published by Clarendon Press. This book was released on 2004-01-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Formalization of Set Theory without Variables by : Alfred Tarski
Download or read book A Formalization of Set Theory without Variables written by Alfred Tarski and published by American Mathematical Soc.. This book was released on 1987 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. This work shows that set theory and number theory can be developed within the framework of a new, different and simple equational formalism, closely related to the formalism of the theory of relation algebras.
Book Synopsis Elements of Set Theory by : Herbert B. Enderton
Download or read book Elements of Set Theory written by Herbert B. Enderton and published by Academic Press. This book was released on 1977-05-23 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Book Synopsis A Book of Set Theory by : Charles C Pinter
Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--
Book Synopsis Set Theory by : Daniel W. Cunningham
Download or read book Set Theory written by Daniel W. Cunningham and published by Cambridge University Press. This book was released on 2016-07-18 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.
Book Synopsis Discrete Mathematical Structures for Computer Science by : Bernard Kolman
Download or read book Discrete Mathematical Structures for Computer Science written by Bernard Kolman and published by Prentice Hall. This book was released on 1987 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text has been designed as a complete introduction to discrete mathematics, primarily for computer science majors in either a one or two semester course. The topics addressed are of genuine use in computer science, and are presented in a logically coherent fashion. The material has been organized and interrelated to minimize the mass of definitions and the abstraction of some of the theory. For example, relations and directed graphs are treated as two aspects of the same mathematical idea. Whenever possible each new idea uses previously encountered material, and then developed in such a way that it simplifies the more complex ideas that follow.
Book Synopsis Set Theory and the Structure of Arithmetic (By> Norman Hamilton (And> Joseph Landin by : Norman Tyson Hamilton
Download or read book Set Theory and the Structure of Arithmetic (By> Norman Hamilton (And> Joseph Landin written by Norman Tyson Hamilton and published by . This book was released on 1964 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory by : Douglas Cenzer
Download or read book Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory written by Douglas Cenzer and published by World Scientific. This book was released on 2020-04-04 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course 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 throughout the text.
Book Synopsis Labyrinth of Thought by : José Ferreirós
Download or read book Labyrinth of Thought written by José Ferreirós and published by Springer Science & Business Media. This book was released on 2008-10-04 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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." --Bulletin of Symbolic Logic (Review of first edition)
Book Synopsis Introduction to Modern Set Theory by : Judith Roitman
Download or read book Introduction to Modern Set Theory written by Judith Roitman and published by John Wiley & Sons. This book was released on 1990-01-16 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.
Book Synopsis Handbook of Set Theory by : Matthew Foreman
Download or read book Handbook of Set Theory written by Matthew Foreman and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 2200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
Book Synopsis Sets for Mathematics by : F. William Lawvere
Download or read book Sets for Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2003-01-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Book Synopsis Philosophical Introduction to Set Theory by : Stephen Pollard
Download or read book Philosophical Introduction to Set Theory written by Stephen Pollard and published by Courier Dover Publications. This book was released on 2015-07-15 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
Book Synopsis Basic Set Theory by : Nikolai Konstantinovich Vereshchagin
Download or read book Basic Set Theory written by Nikolai Konstantinovich Vereshchagin and published by American Mathematical Soc.. This book was released on 2002 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
Book Synopsis Set Theory and the Structure of Arithmetic [by] Norman T. Hamilton [and] Joseph Landin by : Norman Tyson Hamilton
Download or read book Set Theory and the Structure of Arithmetic [by] Norman T. Hamilton [and] Joseph Landin written by Norman Tyson Hamilton and published by . This book was released on with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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