Set Theory Logic And Their Limitations

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Set Theory, Logic and Their Limitations

Author : Moshe Machover
Publisher : Cambridge University Press
Page : 304 pages
File Size : 44,8 Mb
Release : 1996-05-23
Category : Mathematics
ISBN : 0521479983

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Set Theory, Logic and Their Limitations by Moshe Machover Pdf

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

Author : Moshé Machover
Publisher : Unknown
Page : 288 pages
File Size : 40,6 Mb
Release : 1998
Category : Electronic
ISBN : OCLC:629764509

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Set Theory, Logic and Their Limitations by Moshé Machover Pdf

Cantorian Set Theory and Limitation of Size

Author : Michael Hallett
Publisher : Oxford University Press
Page : 372 pages
File Size : 54,6 Mb
Release : 1986
Category : Mathematics
ISBN : 0198532830

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Cantorian Set Theory and Limitation of Size by Michael Hallett Pdf

Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.

Set Theory and Logic

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 50,5 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486139647

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Set Theory and Logic by Robert R. Stoll Pdf

Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.

Set Theory

Author : Daniel W. Cunningham
Publisher : Cambridge University Press
Page : 265 pages
File Size : 55,6 Mb
Release : 2016-07-18
Category : Mathematics
ISBN : 9781107120327

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Set Theory by Daniel W. Cunningham Pdf

Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.

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

Author : Igor Lavrov,Larisa Maksimova
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 50,9 Mb
Release : 2003-03-31
Category : Mathematics
ISBN : 0306477122

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Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by Igor Lavrov,Larisa Maksimova Pdf

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.

Naive Set Theory

Author : Paul Richard Halmos
Publisher : Unknown
Page : 122 pages
File Size : 46,8 Mb
Release : 1960
Category : Mathematics
ISBN : UOM:39015006570702

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Naive Set Theory by Paul Richard Halmos Pdf

From the Reviews: .,."He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know. ...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics." Philosophy and Phenomenological Research

Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory

Author : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Publisher : World Scientific
Page : 222 pages
File Size : 49,9 Mb
Release : 2020-04-04
Category : Mathematics
ISBN : 9789811201943

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Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory by Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal Pdf

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.

The Outer Limits of Reason

Author : Noson S. Yanofsky
Publisher : MIT Press
Page : 419 pages
File Size : 49,9 Mb
Release : 2016-11-04
Category : Science
ISBN : 9780262529846

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The Outer Limits of Reason by Noson S. Yanofsky Pdf

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.

Introduction to Model Theory

Author : Philipp Rothmaler
Publisher : CRC Press
Page : 324 pages
File Size : 51,9 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429668500

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Introduction to Model Theory by Philipp Rothmaler Pdf

Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.

Lectures in Logic and Set Theory: Volume 2, Set Theory

Author : George Tourlakis
Publisher : Cambridge University Press
Page : 596 pages
File Size : 45,6 Mb
Release : 2003-02-13
Category : Mathematics
ISBN : 113943943X

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Lectures in Logic and Set Theory: Volume 2, Set Theory by George Tourlakis Pdf

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.

The Logic of Infinity

Author : Barnaby Sheppard
Publisher : Cambridge University Press
Page : 498 pages
File Size : 52,5 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9781107058316

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The Logic of Infinity by Barnaby Sheppard Pdf

This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.

The Foundations of Computability Theory

Author : Borut Robič
Publisher : Springer
Page : 331 pages
File Size : 44,5 Mb
Release : 2015-09-14
Category : Computers
ISBN : 9783662448083

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The Foundations of Computability Theory by Borut Robič Pdf

This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.

Numbers, Sets and Axioms

Author : A. G. Hamilton
Publisher : Cambridge University Press
Page : 272 pages
File Size : 41,8 Mb
Release : 1982
Category : Mathematics
ISBN : 0521287618

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Numbers, Sets and Axioms by A. G. Hamilton Pdf

Following the success of Logic for Mathematicians, Dr Hamilton has written a text for mathematicians and students of mathematics that contains a description and discussion of the fundamental conceptual and formal apparatus upon which modern pure mathematics relies. The author's intention is to remove some of the mystery that surrounds the foundations of mathematics. He emphasises the intuitive basis of mathematics; the basic notions are numbers and sets and they are considered both informally and formally. The role of axiom systems is part of the discussion but their limitations are pointed out. Formal set theory has its place in the book but Dr Hamilton recognises that this is a part of mathematics and not the basis on which it rests. Throughout, the abstract ideas are liberally illustrated by examples so this account should be well-suited, both specifically as a course text and, more broadly, as background reading. The reader is presumed to have some mathematical experience but no knowledge of mathematical logic is required.

Logic and Relational Theory

Author : C. J. Date
Publisher : Technics Publications
Page : 336 pages
File Size : 50,8 Mb
Release : 2020-06-06
Category : Computers
ISBN : 9781634628778

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Logic and Relational Theory by C. J. Date Pdf

This book is a revised, upgraded, and hugely improved version of an earlier one called Logic and Databases. Although it’s effectively a brand new book, therefore, the following remarks from that earlier book are still relevant here. First, logic and databases are inextricably intertwined. The relational model itself is essentially just elementary logic, tailored to database needs. Now, if you’re a database professional, this won’t be news to you—but you still might not realize just how much everything we do in the database world is (or should be!) affected by logic. Logic is fundamental, and everywhere. As a database professional, therefore, you owe it to yourself to understand the basics of formal logic, and you ought to be able to explain (and perhaps defend) the connections between formal logic and database technology. And that’s what this book is about. What it does is show, through a series of partly independent, partly interrelated essays, just how various crucial aspects of database technology—some of them very familiar, others maybe less so—are solidly grounded in formal logic. Overall, the goal is to help you realize the importance of logic in everything you do, and also, I hope, to help you see that logic can be fun.