Set Theory And Its Logic
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| Author | : Willard Van O QUINE |
| Publisher | : Harvard University Press |
| Total Pages | : 381 |
| Release | : 2009-06-30 |
| Genre | : Philosophy |
| ISBN | : 0674042425 |
Download Set Theory and Its Logic, Revised Edition Book in PDF, Epub and Kindle
This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
| Author | : Robert R. Stoll |
| Publisher | : Courier Corporation |
| Total Pages | : 516 |
| Release | : 2012-05-23 |
| Genre | : Mathematics |
| ISBN | : 0486139646 |
Download Set Theory and Logic Book in PDF, Epub and Kindle
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.
| Author | : Moshe Machover |
| Publisher | : Cambridge University Press |
| Total Pages | : 304 |
| Release | : 1996-05-23 |
| Genre | : Mathematics |
| ISBN | : 9780521479981 |
Download Set Theory, Logic and Their Limitations Book in PDF, Epub and Kindle
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.
| Author | : Michael Potter |
| Publisher | : Clarendon Press |
| Total Pages | : 362 |
| Release | : 2004-01-15 |
| Genre | : Philosophy |
| ISBN | : 0191556432 |
Download Set Theory and its Philosophy Book in PDF, Epub and Kindle
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
| Author | : Jacob T. Schwartz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 426 |
| Release | : 2011-07-16 |
| Genre | : Computers |
| ISBN | : 0857298089 |
Download Computational Logic and Set Theory Book 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.
| Author | : Raymond M. Smullyan |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2010 |
| Genre | : Continuum hypothesis |
| ISBN | : 9780486474847 |
Download Set Theory and the Continuum Problem Book in PDF, Epub and Kindle
A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.
| Author | : J. Barkley Rosser |
| Publisher | : Courier Dover Publications |
| Total Pages | : 587 |
| Release | : 2008-12-18 |
| Genre | : Mathematics |
| ISBN | : 0486468984 |
Download Logic for Mathematicians Book in PDF, Epub and Kindle
Examination of essential topics and theorems assumes no background in logic. "Undoubtedly a major addition to the literature of mathematical logic." — Bulletin of the American Mathematical Society. 1978 edition.
| Author | : P. T. Johnstone |
| Publisher | : Cambridge University Press |
| Total Pages | : 128 |
| Release | : 1987-10-08 |
| Genre | : Mathematics |
| ISBN | : 9780521335027 |
Download Notes on Logic and Set Theory Book 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.
| Author | : Peter J. Cameron |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 191 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1447105893 |
Download Sets, Logic and Categories Book in PDF, Epub and Kindle
Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.
| Author | : Norman T. Hamilton |
| Publisher | : Courier Dover Publications |
| Total Pages | : 289 |
| Release | : 2018-05-16 |
| Genre | : Mathematics |
| ISBN | : 0486830470 |
Download Set Theory: The Structure of Arithmetic Book in PDF, Epub and Kindle
This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.
