Lectures In Logic And Set Theory Volume 2 Set Theory
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Lectures in Logic and Set Theory Volume 2 Set Theory
Author | : George Tourlakis |
Publsiher | : Cambridge University Press |
Total Pages | : 596 |
Release | : 2003-02-13 |
Genre | : Mathematics |
ISBN | : 113943943X |
Download Lectures in Logic and Set Theory Volume 2 Set Theory Book in PDF, Epub and Kindle
This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.
Lectures in Logic and Set Theory Volume 2 Set Theory
Author | : George Tourlakis |
Publsiher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 2003-02-13 |
Genre | : Mathematics |
ISBN | : 0521753740 |
Download Lectures in Logic and Set Theory Volume 2 Set Theory Book in PDF, Epub and Kindle
Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).
Lectures in Logic and Set Theory
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 575 |
Release | : 2003 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : OCLC:70773621 |
Download Lectures in Logic and Set Theory Book in PDF, Epub and Kindle
Lectures in Logic and Set Theory Volume 1 Mathematical Logic
Author | : George Tourlakis |
Publsiher | : Cambridge University Press |
Total Pages | : 344 |
Release | : 2003-01-09 |
Genre | : Mathematics |
ISBN | : 9781139439428 |
Download Lectures in Logic and Set Theory Volume 1 Mathematical Logic Book in PDF, Epub and Kindle
This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.
An Introduction to Proofs with Set Theory
Author | : Daniel Ashlock,Colin Lee |
Publsiher | : Morgan & Claypool Publishers |
Total Pages | : 251 |
Release | : 2020-06-24 |
Genre | : Mathematics |
ISBN | : 9781681738802 |
Download An Introduction to Proofs with Set Theory Book in PDF, Epub and Kindle
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
Author | : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal |
Publsiher | : World Scientific |
Total Pages | : 222 |
Release | : 2020-04-04 |
Genre | : Mathematics |
ISBN | : 9789811201943 |
Download Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory Book in PDF, Epub and Kindle
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.
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics
Author | : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal |
Publsiher | : World Scientific |
Total Pages | : 254 |
Release | : 2022-01-27 |
Genre | : Mathematics |
ISBN | : 9789811243868 |
Download Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics Book in PDF, Epub and Kindle
This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Gödel's Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy.
Concise Introduction to Logic and Set Theory
Author | : Iqbal H. Jebril,Hemen Dutta,Ilwoo Cho |
Publsiher | : CRC Press |
Total Pages | : 168 |
Release | : 2021-10-14 |
Genre | : Technology & Engineering |
ISBN | : 9780429663260 |
Download Concise Introduction to Logic and Set Theory Book in PDF, Epub and Kindle
This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology.