An Invitation to Mathematical 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 An Invitation to Mathematical Logic write by David Marker. This book was released on 2024-05-14. An Invitation to Mathematical Logic available in PDF, EPUB and Kindle. In addition to covering the essentials, the author’s intention in writing this text is to entice the reader to further study mathematical logic. There is no current “standard text” for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks’ worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives. This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading. New definitions, formalism, and syntax have been streamlined to engage the reader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16. For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed.
An Invitation to Model Theory
An Invitation to Model 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 An Invitation to Model Theory write by Jonathan Kirby. This book was released on 2019-04-18. An Invitation to Model Theory available in PDF, EPUB and Kindle. Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
Mathematical Logic
Mathematical 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 Mathematical Logic write by H.-D. Ebbinghaus. This book was released on 2013-03-14. Mathematical Logic available in PDF, EPUB and Kindle. This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
A Logical Foundation for Potentialist Set Theory
A Logical Foundation for Potentialist 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 Logical Foundation for Potentialist Set Theory write by Sharon Berry. This book was released on 2022-02-17. A Logical Foundation for Potentialist Set Theory available in PDF, EPUB and Kindle. A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.
Mathematical Logic and Model Theory
Mathematical Logic and Model 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 Mathematical Logic and Model Theory write by Alexander Prestel. This book was released on 2011-08-21. Mathematical Logic and Model Theory available in PDF, EPUB and Kindle. 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.
