This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, categoricity, automorphisms, and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given, followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation, nonstandard models of arithmetic, Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth, and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.

The two-volume set originates from the Advanced Course on Petri Nets held in Dagstuhl, Germany in September 1996; beyond the lectures given there, additional chapters have been commissioned to give a well-balanced presentation of the state of the art in the area. Together with its companion volume "Lectures on Petri Nets II: Applications" this book is the actual reference for the area and addresses professionals, students, lecturers, and researchers who are - interested in systems design and would like to learn to use Petri nets familiar with subareas of the theory or its applications and wish to view the whole area - interested in learning about recent results presented within a unified framework - planning to apply Petri nets in practical situations - interested in the relationship of Petri nets to other models of concurrent systems.

This thin volume contains three sets of lecture notes, representing recent developments in differential scales, o-minimality, and tame convergence theory. The first lecture outlines the basics of differential fields, and then addresses topics like differential varieties and tangent bundles, Kolchin's logarithmic derivative, and Manin's construction. The second describes added exponentation, T-convexity and tame extensions, piecewise linearity, the Wilkie inequality, and the valuation property. And the third considers the structure and varieties of finite algebra. No index. c. Book News Inc.

A Collection of Lectures by Variuos Authors

Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Category Theory is one of the most abstract branches of mathematics. It is usually taught to graduate students after they have mastered several other branches of mathematics, like algebra, topology, and group theory. It might, therefore, come as a shock that the basic concepts of category theory can be explained in relatively simple terms to anybody with some experience in programming.That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Well-structured programs are easier to understand and maintain and are less likely to contain bugs. Category theory provides the language to talk about structure and learning it will make you a better programmer.

Sir Richard Owen (1804-1892), comparative anatomist, colleague and later antagonist of Darwin, and head of the British Museum of Natural History, was a major figure in Victorian science. Yet historians of science have found Owen a difficult subject, in part because he chose not to expound his views in a major theoretical work but rather presented them through annual lectures at the Royal College of Surgeons from 1837 to 1856. Nevertheless, Owen's views on the nature of life, the relations of form and function, the meaning of fossils, and the development of species gave his contemporaries such as Lyell, Grant, Huxley, Whewell, and Darwin a set of positions with which they could agree or disagree while developing their own views. Now, for the first time, modern readers how access to the opening series of Owen's Hunterian Lectures, in which he set out the larger framework of the theoretical reflections that occupied him during the next nineteen years. Presented to the public in the two months before Darwin began his first notebook on the species question, these lectures reveal the nature of the synthesis of French, German, and British biology taking place in metropolitan London in this crucial period in nineteenth-century life science. Phillip Reid Sloan has transcribed and edited the seven surviving lectures and has written an introduction and commentary situating the work in the context of Owen's life and the scientific and intellectual life of the time. Sloan pays particular attention to Owen's early relations to the German scientific and philosophical tradition, and in this respect contributes to an understanding of the relations between science and British Romanticism. In the lectures, Owen surveys the history of comparative anatomy up to his time and develops his views on the nature of life, species duration, physiological function, and the relation between embryology and classification. One can see the degree to which transcendental anatomy and the views of Von Baer, Johannes Müller, E. G. St.-Hilaire, and Cuvier were current in London in the late 1830s. -- from back cover.

The European Summer School in Logic, Language and Information (ESSLLI) is organized every year by the Association for Logic, Language and Information (FoLLI) in different sites around Europe. The main focus of ESSLLI is on the interface between linguistics, logic and computation. ESSLLI offers foundational, introductory and advanced courses, as well as workshops, covering a wide variety of topics within the three areas of interest: Language and Computation, Language and Logic, and Logic and Computation. During two weeks, around 50 courses and 10 workshops are offered to the attendants, each of 1.5 hours per day during a five days week, with up to seven parallel sessions. ESSLLI also includes a student session (papers and posters by students only, 1.5 hour per day during the two weeks) and four evening lectures by senior scientists in the covered areas. The 6 course notes were carefully reviewed and selected. The papers are organized in topical sections on computational complexity, multi-agant systems, natural language processing, strategies in games and formal semantics.