Notes on Logic and Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Notes on Logic and Set Theory write by P. T. Johnstone. This book was released on 1987-10-08. Notes on Logic and Set Theory available in PDF, EPUB and Kindle. 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.
Notes on Set Theory
Notes on Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Notes on Set Theory write by Yiannis Moschovakis. This book was released on 2013-04-17. Notes on Set Theory available in PDF, EPUB and Kindle. What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
Computational Logic and Set Theory
Computational Logic and Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Logic and Set Theory write by Jacob T. Schwartz. This book was released on 2011-07-16. Computational Logic and Set Theory available in PDF, EPUB and Kindle. This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.
Concise Introduction to Logic and Set Theory
Concise Introduction to Logic and Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Concise Introduction to Logic and Set Theory write by Iqbal H. Jebril. This book was released on 2021-09-30. Concise Introduction to Logic and Set Theory available 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.
Notes on Logic and Set Theory
Notes on Logic and Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Notes on Logic and Set Theory write by P. T. Johnstone. This book was released on 1987-10-08. Notes on Logic and Set Theory available in PDF, EPUB and Kindle. This short textbook provides a succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. It will be suitable for all mathematics undergraduates coming to the subject for the first time. The book is based on lectures given at the University of Cambridge and 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. There are also chapters on 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. Consequently the book, while making an attractive first textbook for those who plan to specialise in logic, will be particularly valuable for mathematics and computer scientists whose primary interests lie elsewhere.
