Set Theory and Logic - 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 Set Theory and Logic write by Robert R. Stoll. This book was released on 2012-05-23. Set Theory and Logic available 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.
Set Theory, Logic and Their Limitations
Set Theory, Logic and Their Limitations - 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 Set Theory, Logic and Their Limitations write by Moshe Machover. This book was released on 1996-05-23. Set Theory, Logic and Their Limitations available 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.
Logic for Mathematicians
Logic for Mathematicians - 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 Logic for Mathematicians write by J. Barkley Rosser. This book was released on 2008-12-18. Logic for Mathematicians available 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.
Sets, Logic and Categories
Sets, Logic and Categories - 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 Sets, Logic and Categories write by Peter J. Cameron. This book was released on 2012-12-06. Sets, Logic and Categories available 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.
A First Course in Mathematical Logic and Set Theory
A First Course in Mathematical 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 A First Course in Mathematical Logic and Set Theory write by Michael L. O'Leary. This book was released on 2015-09-14. A First Course in Mathematical Logic and Set Theory available in PDF, EPUB and Kindle. A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
