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Set Theory, Logic and Their Limitations

1996-05-23 Mathematics
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Release : 1996-05-23
Genre : Mathematics
Kind : eBook
Book Rating : 981/5 ( reviews)

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Book Synopsis Set Theory, Logic and Their Limitations by : Moshe Machover

Download or read book Set Theory, Logic and Their Limitations written by Moshe Machover. This book was released on 1996-05-23. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

Set Theory, Logic and Their Limitations

1998
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Release : 1998
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Set Theory, Logic and Their Limitations by : Moshé Machover

Download or read book Set Theory, Logic and Their Limitations written by Moshé Machover. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt:

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms

2003-03-31 Mathematics
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Release : 2003-03-31
Genre : Mathematics
Kind : eBook
Book Rating : 126/5 ( reviews)

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Book Synopsis Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by : Igor Lavrov

Download or read book Problems in Set Theory, Mathematical Logic and the Theory of Algorithms written by Igor Lavrov. This book was released on 2003-03-31. Available in PDF, EPUB and Kindle. Book excerpt: Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.

The Outer Limits of Reason

2016-11-04 Science
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Release : 2016-11-04
Genre : Science
Kind : eBook
Book Rating : 84X/5 ( reviews)

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Book Synopsis The Outer Limits of Reason by : Noson S. Yanofsky

Download or read book The Outer Limits of Reason written by Noson S. Yanofsky. This book was released on 2016-11-04. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

A Book of Set Theory

2014-07-23 Mathematics
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Release : 2014-07-23
Genre : Mathematics
Kind : eBook
Book Rating : 089/5 ( reviews)

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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. This book was released on 2014-07-23. 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"--

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