Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.
This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.
Mathematics by A. Ehrenfeucht,V.W. Marek,M. Srebrny
Andrzej Mostowski was one of the leading 20th century logicians. His legacy is examined in this volume of papers devoted both to his extraordinary scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and person. Professor Mostowski pioneered and mastered many areas of mathematical logic. His contributions spanned set theory, recursion theory, and model theory - the backbone of the foundations of mathematics. The complete detailed bibliography of Mostowski's writings is included. For many years after WWII and especially in the late sixties and until his untimely death in 1975, Warsaw, where he led the centre of foundational studies, was a place where many leading logicians visited, studied, and started their career. Their memories form an important part of this volume, attempting to bring back the extraordinary achievements and personality of Mostowski.
Computers by Jan A Bergstra,Cornelis A. Middelburg
This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all.
A unified, coherent account of the algebraic aspects and uses of the Ziegler spectrum. It may be used as an introductory graduate-level text, providing relevant background material and a wealth of illustrated examples. An extensive index and thorough referencing also make this book an ideal reference.
Newer Applications to Algebraic Topology, Descriptive Sets, and Computing Categories Topos
Author: Cyrus F. Nourani
Publisher: CRC Press
This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic, held October 18-22, 2003
Author: Ali Enayat,Iraj Kalantari,Mojtaba Moniri
Publisher: A K Peters Ltd
This collection of papers is based on a conference that was held in Tehran, Iran, with the express purpose of bringing together researchers with connections to Iranian logicians and promoting further research in mathematical logic in Iran. Particular emphasis was given to model theory and its applications to algebra and formal theories of arithmetic. Other papers address category theory, computability, modal logic, and the history of mathematical logic in Iran.
Mathematical Models is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Mathematical Models discusses matters of great relevance to our world such as: Basic Principles of Mathematical Modeling; Mathematical Models in Water Sciences; Mathematical Models in Energy Sciences; Mathematical Models of Climate and Global Change; Infiltration and Ponding; Mathematical Models of Biology; Mathematical Models in Medicine and Public Health; Mathematical Models of Society and Development. These three volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.
Mathematical statistics by Samuel Kotz,N. Balakrishnan
Entries cover statistical theory, methods, and applications. Includes the latest topics and advances made in statistical science over the past decade--in areas such as computer-intensive statistical methodology, genetics, medicine, the environment, and other applications.
Education is a field sometimes beset by theories-of-the-day and with easy panaceas that overpromise the degree to which they can alleviate pressing educational problems. The two-volume Encyclopedia of Educational Theory and Philosophy introduces readers to theories that have stood the test of time and those that have provided the historical foundation for the best of contemporary educational theory and practice. Drawing together a team of international scholars, this invaluable reference examines the global landscape of all the key theories and the theorists behind them and presents them in the context needed to understand their strengths and weaknesses. In addition to interpretations of long-established theories, this work offers essays on cutting-edge research and concise, to-the-point definitions of key concepts, ideas, schools, and figures. Features: Over 300 signed entries by trusted experts in the field are organized into two volumes and overseen by a distinguished General Editor and an international Editorial Board. Entries are followed by cross references and further reading suggestions. A Chronology of Theory within the field of education highlights developments over the centuries; a Reader’s Guide groups entries thematically, and a master Bibliography facilitates further study. The Reader’s Guide, detailed index, and cross references combine for strong search-and-browse capabilities in the electronic version. Available in a choice of print or electronic formats, Encyclopedia of Educational Theory and Philosophy is an ideal reference for anyone interested in the roots of contemporary educational theory.
Mathematics by Robin Ticciati,Robin (Maharishi University of Management Ticciati, Iowa)