Notes On Set Theory
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Notes On Set Theory
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Author : Yiannis Moschovakis
language : en
Publisher:
Release Date : 2014-01-15
Notes On Set Theory written by Yiannis Moschovakis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Notes On Logic And Set Theory
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Author : P. T. Johnstone
language : en
Publisher: Cambridge University Press
Release Date : 1987-10-08
Notes On Logic And Set Theory written by P. T. Johnstone 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 1987-10-08 with Mathematics categories.
A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.
Handbook Of Set Theoretic Topology
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Author : Kenneth Kunen
language : en
Publisher: North-Holland
Release Date : 1984
Handbook Of Set Theoretic Topology written by Kenneth Kunen and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhaacute;sz on cardinal functions; Roitman and Abraham-Todorccaron;evicacute; on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.
Notes On Set Theory
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Author : Yiannis N. Moschovakis
language : en
Publisher: Springer
Release Date : 1994
Notes On Set Theory written by Yiannis N. Moschovakis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Axiomatische Mengenlehre categories.
The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation.
An Introduction To Proofs With Set Theory
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Author : Daniel Ashlock
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
An Introduction To Proofs With Set Theory written by Daniel Ashlock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.
This text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid's algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor's Paradox, Russel's Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of Gödel's Incompleteness Theorems.
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory Second Edition
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Author : Douglas Cenzer
language : en
Publisher: World Scientific
Release Date : 2025-01-10
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory Second Edition written by Douglas Cenzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-10 with Mathematics categories.
This book presents both axiomatic and descriptive set theory, targeting upper-level undergraduate and beginning graduate students. It aims to equip them for advanced studies in set theory, mathematical logic, and other mathematical fields, including analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory 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 through the text.This new edition includes additional topics on trees, ordinal functions, and sets, along with numerous new exercises. The presentation has been improved, and several typographical errors have been corrected.
Basic Set Theory
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Author : Nikolai Konstantinovich Vereshchagin
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Basic Set Theory written by Nikolai Konstantinovich Vereshchagin 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 2002 with Mathematics categories.
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.
Notes On The Nicomachean Ethics Of Aristotle
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Author : John Alexander Stewart
language : en
Publisher:
Release Date : 1892
Notes On The Nicomachean Ethics Of Aristotle written by John Alexander Stewart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1892 with categories.
Elements Of Set Theory
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Author : Herbert B. Enderton
language : en
Publisher: Gulf Professional Publishing
Release Date : 1977-04-28
Elements Of Set Theory written by Herbert B. Enderton and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-04-28 with Mathematics categories.
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.
The Bulletin Of Mathematics Books
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Author :
language : en
Publisher:
Release Date : 1992
The Bulletin Of Mathematics Books written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computer software categories.