Models Algebras And Proofs

Author : Xavier Caicedo
Publisher : CRC Press
ISBN 13 : 9780824719708
Total Pages : 474 pages
Book Rating : 4.00/5 ( download)

DOWNLOAD NOW!

Download or read book Models, Algebras, and Proofs written by Xavier Caicedo and published by CRC Press. This book was released on 1998-11-05 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide."

Author : Ieke Moerdijk
Publisher : Springer
ISBN 13 : 3319924141
Total Pages : 141 pages
Book Rating : 4.44/5 ( download)

DOWNLOAD NOW!

Download or read book Sets, Models and Proofs written by Ieke Moerdijk and published by Springer. This book was released on 2018-11-23 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.

Author : Xavier Caicedo
Publisher : CRC Press
ISBN 13 : 1000657302
Total Pages : 470 pages
Book Rating : 4.02/5 ( download)

DOWNLOAD NOW!

Download or read book Models, Algebras, and Proofs written by Xavier Caicedo and published by CRC Press. This book was released on 2021-02-28 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts.

Author : Paul Halmos
Publisher : American Mathematical Soc.
ISBN 13 : 1470451662
Total Pages : 141 pages
Book Rating : 4.60/5 ( download)

DOWNLOAD NOW!

Download or read book Logic as Algebra written by Paul Halmos and published by American Mathematical Soc.. This book was released on 2019-01-30 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed.

Author : John L. Bell
Publisher : Oxford University Press
ISBN 13 : 0199609160
Total Pages : 214 pages
Book Rating : 4.61/5 ( download)

DOWNLOAD NOW!

Download or read book Set Theory written by John L. Bell and published by Oxford University Press. This book was released on 2011-05-05 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.

Author : David Marker
Publisher : Springer Science & Business Media
ISBN 13 : 0387227342
Total Pages : 342 pages
Book Rating : 4.44/5 ( download)

DOWNLOAD NOW!

Download or read book Model Theory : An Introduction written by David Marker and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures

Author : Alexander Prestel
Publisher : Springer Science & Business Media
ISBN 13 : 1447121767
Total Pages : 198 pages
Book Rating : 4.63/5 ( download)

DOWNLOAD NOW!

Download or read book Mathematical Logic and Model Theory written by Alexander Prestel and published by Springer Science & Business Media. This book was released on 2011-08-21 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.

Author : Thorsten Altenkirch
Publisher : Springer
ISBN 13 : 3540744649
Total Pages : 277 pages
Book Rating : 4.41/5 ( download)

DOWNLOAD NOW!

Download or read book Types for Proofs and Programs written by Thorsten Altenkirch and published by Springer. This book was released on 2007-09-13 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refereed post-proceedings of the International Workshop of the Types Working Group are presented in this volume. The 17 papers address all current issues in formal reasoning and computer programming based on type theory, including languages and computerized tools for reasoning; applications in several domains, such as analysis of programming languages; certified software; formalization of mathematics; and mathematics education.

Author : Zofia Adamowicz
Publisher : John Wiley & Sons
ISBN 13 : 1118030796
Total Pages : 276 pages
Book Rating : 4.90/5 ( download)

DOWNLOAD NOW!

Download or read book Logic of Mathematics written by Zofia Adamowicz and published by John Wiley & Sons. This book was released on 2011-09-26 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.

Author : W Felscher
Publisher : CRC Press
ISBN 13 : 9789056992668
Total Pages : 298 pages
Book Rating : 4.6X/5 ( download)

DOWNLOAD NOW!

Download or read book Set Theoretical Logic-The Algebra of Models written by W Felscher and published by CRC Press. This book was released on 2000-05-30 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to mathematical logic in which all the usual topics are presented: compactness and axiomatizability of semantical consequence, Löwenheim-Skolem-Tarski theorems, prenex and other normal forms, and characterizations of elementary classes with the help of ultraproducts. Logic is based exclusively on semantics: truth and satisfiability of formulas in structures are the basic notions. The methods are algebraic in the sense that notions such as homomorphisms and congruence relations are applied throughout in order to gain new insights. These concepts are developed and can be viewed as a first course on universal algebra. The approach to algorithms generating semantical consequences is algebraic as well: for equations in algebras, for propositional formulas, for open formulas of predicate logic, and for the formulas of quantifier logic. The structural description of logical consequence is a straightforward extension of that of equational consequence, as long as Boolean valued propositions and Boolean valued structures are considered; the reduction of the classical 2-valued case then depends on the Boolean prime ideal theorem.