Download or read book Simple Theories and Hyperimaginaries written by Enrique Casanovas and published by Cambridge University Press. This book was released on 2011-06-30 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1990s Kim and Pillay generalized stability, a major model theoretic idea developed by Shelah twenty-five years earlier, to the study of simple theories. This book is an up-to-date introduction to simple theories and hyperimaginaries, with special attention to Lascar strong types and elimination of hyperimaginary problems. Assuming only knowledge of general model theory, the foundations of forking, stability, and simplicity are presented in full detail. The treatment of the topics is as general as possible, working with stable formulas and types and assuming stability or simplicity of the theory only when necessary. The author offers an introduction to independence relations as well as a full account of canonical bases of types in stable and simple theories. In the last chapters the notions of internality and analyzability are discussed and used to provide a self-contained proof of elimination of hyperimaginaries in supersimple theories.
Download or read book Simplicity Theory written by Byunghan Kim and published by Oxford Logic Guides. This book was released on 2014 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date account of the current techniques and results in Simplicity Theory, which has been a focus of research in model theory for the last decade. Suitable for logicians, mathematicians and graduate students working on model theory.
Download or read book Models and Computability written by S. Barry Cooper and published by Cambridge University Press. This book was released on 1999-06-17 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second of two volumes providing a comprehensive guide to the current state of mathematical logic.
Download or read book A Course on Basic Model Theory written by Haimanti Sarbadhikari and published by Springer. This book was released on 2017-09-05 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book is an exposition of the fundamental ideas of model theory. It presents the necessary background from logic, set theory and other topics of mathematics. Only some degree of mathematical maturity and willingness to assimilate ideas from diverse areas are required. The book can be used for both teaching and self-study, ideally over two semesters. It is primarily aimed at graduate students in mathematical logic who want to specialise in model theory. However, the first two chapters constitute the first introduction to the subject and can be covered in one-semester course to senior undergraduate students in mathematical logic. The book is also suitable for researchers who wish to use model theory in their work.
Download or read book The Bulletin of Symbolic Logic written by and published by . This book was released on 2005 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Groups and Model Theory written by Olga Kharlampovich and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-05-10 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .
Download or read book Topics In Model Theory written by Anand Pillay and published by World Scientific. This book was released on 2024-04-29 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has two chapters. The first is a modern or contemporary account of stability theory. A focus is on the local (formula-by-formula) theory, treated a little differently from in the author's book Geometric Stability Theory. There is also a survey of general and geometric stability theory, as well as applications to combinatorics (stable regularity lemma) using pseudofinite methods.The second is an introduction to 'continuous logic' or 'continuous model theory,' drawing on the main texts and papers, but with an independent point of view. This chapter includes some historical background, including some other formalisms for continuous logic and a discussion of hyperimaginaries in classical first order logic.These chapters are based around notes, written by students, from a couple of advanced graduate courses in the University of Notre Dame, in Autumn 2018, and Spring 2021.
Download or read book A Guide to NIP Theories written by Pierre Simon and published by Cambridge University Press. This book was released on 2015-07-16 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of NIP theories has received much attention from model theorists in the last decade, fuelled by applications to o-minimal structures and valued fields. This book, the first to be written on NIP theories, is an introduction to the subject that will appeal to anyone interested in model theory: graduate students and researchers in the field, as well as those in nearby areas such as combinatorics and algebraic geometry. Without dwelling on any one particular topic, it covers all of the basic notions and gives the reader the tools needed to pursue research in this area. An effort has been made in each chapter to give a concise and elegant path to the main results and to stress the most useful ideas. Particular emphasis is put on honest definitions, handling of indiscernible sequences and measures. The relevant material from other fields of mathematics is made accessible to the logician.
Download or read book Thorn Forking in Simple Theories and a Manin Mumford Theorem for T modules written by Clifton F. Ealy and published by . This book was released on 2004 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Course in Model Theory written by Katrin Tent and published by Cambridge University Press. This book was released on 2012-03-08 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise introduction to current topics in model theory, including simple and stable theories.
Download or read book Logic Colloquium 01 written by Matthias Baaz and published by Cambridge University Press. This book was released on 2017-03-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twentieth publication in the Lecture Notes in Logic series, contains the proceedings of the 2001 European Summer Meeting of the Association for Symbolic Logic, held at the Vienna University of Technology. Two long articles present accessible expositions on resolution theorem proving and the determinacy of long games. The remaining articles cover separate research topics in many areas of mathematical logic, including applications in computer science, proof theory, set theory, model theory, computability theory, linguistics and aspects of philosophy. This collection will interest not only mathematical logicians but also philosophical logicians, historians of logic, computer scientists, formal linguists and mathematicians working in algebra, abstract analysis and topology.
Download or read book Simple Theories written by Frank Olaf Wagner and published by Springer. This book was released on 2010-12-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simplicity theory is an extension of stability theory to a wider class of structures, containing, among others, the random graph, pseudo-finite fields, and fields with a generic automorphism. Following Kim's proof of `forking symmetry' which implies a good behaviour of model-theoretic independence, this area of model theory has been a field of intense study. It has necessitated the development of some important new tools, most notably the model-theoretic treatment of hyperimaginaries (classes modulo type-definable equivalence relations). It thus provides a general notion of independence (and of rank in the supersimple case) applicable to a wide class of algebraic structures. The basic theory of forking independence is developed, and its properties in a simple structure are analyzed. No prior knowledge of stability theory is assumed; in fact many stability-theoretic results follow either from more general propositions, or are developed in side remarks. Audience: This book is intended both as an introduction to simplicity theory accessible to graduate students with some knowledge of model theory, and as a reference work for research in the field.
Download or read book A Guide to NIP Theories written by Pierre Simon and published by Cambridge University Press. This book was released on 2015-07-16 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.
Download or read book Logic in Tehran written by Ali Enayat and published by Cambridge University Press. This book was released on 2017-03-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-sixth publication in the Lecture Notes in Logic series, contains the proceedings of the 'Workshop and Conference on Logic, Algebra and Arithmetic' held at the Institute for Studies in Theoretical Physics and Mathematics (IPM) in Tehran, Iran in October, 2003. These papers are mostly revised and expanded versions of those that were originally presented at the meeting and address all areas of mathematical logic. The book also includes a short history of mathematical logic in Iran.
Download or read book Proceedings of the 10th Asian Logic Conference Kobe Japan 1 6 September 2008 written by Toshiyasu Arai and published by World Scientific. This book was released on 2010 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 10th Asian Logic Conference is part of the series of logic conferences inaugurated in Singapore in 1981. This meeting is held every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association of Symbolic Logic. This volume contains papers from the 10th meeting held in Kobe, Japan.
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Tarskian Turn written by Leon Horsten and published by MIT Press. This book was released on 2011-07-15 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: A philosopher proposes a new deflationist view of truth, based on contemporary proof-theoretic approaches. In The Tarskian Turn, Leon Horsten investigates the relationship between formal theories of truth and contemporary philosophical approaches to truth. The work of mathematician and logician Alfred Tarski (1901–1983) marks the transition from substantial to deflationary views about truth. Deflationism—which holds that the notion of truth is light and insubstantial—can be and has been made more precise in multiple ways. Crucial in making the deflationary intuition precise is its relation to formal or logical aspects of the notion of truth. Allowing that semantical theories of truth may have heuristic value, in The Tarskian Turn Horsten focuses on axiomatic theories of truth developed since Tarski and their connection to deflationism. Arguing that the insubstantiality of truth has been misunderstood in the literature, Horsten proposes and defends a new kind of deflationism, inferential deflationism, according to which truth is a concept without a nature or essence. He argues that this way of viewing the concept of truth, inspired by a formalization of Kripke's theory of truth, flows naturally from the best formal theories of truth that are currently available. Alternating between logical and philosophical chapters, the book steadily progresses toward stronger theories of truth. Technicality cannot be altogether avoided in the subject under discussion, but Horsten attempts to strike a balance between the need for logical precision on the one hand and the need to make his argument accessible to philosophers.
