Bøger i Oxford Logic Guides serien

Pratt-Hartmann considers for which fragments of first-order logic there is an effective method for determining satisfiability or finite satisfiability. Furthermore, he asks, if these problems are decidable for some fragment, what is their computational complexity?

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.

A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.

A monograph on the interface of computational complexity and randomness of sets of natural numbers.

Stewart Shapiro presents a distinctive original view of the foundations of mathematics, arguing that second-order logic has a central role to play in laying these foundations. He gives an accessible account of second-order and higher-order logic, paying special attention to philosophical and historical issues.

Topos theory provides an important setting and language for much of mathematical logic and set theory. This book presents a convenient and natural solution to the treatment of geometric morphisms in this setting and shows how this may be applied to topics such as the relative Giraud theorem.

An introduction to the developments of nonstandard models. Beginning with Godel's incompleteness theorem, it covers the prime models, cofinal extensions, and extensions, Gaifman's construction of a definable type, Tennenbaum's theorem and Friedman's theorem on indicators, ending with a chapter on recursive saturation and resplendency.

BL Indispensable reference for both the pure logician and the theoretical computer scientistThis long awaited book gives a thorough account of the mathematical foundations of Temporal Logic, one of the most important areas of logic in computer science.

BL An introduction to the topic - pitched at an elementary level This Oxford Logic Guide presents a unified treatment of fixed points, self-reference, and diagonalization as they occur in Goedel's incompleteness proofs, recursion theory, combinatory logics, semantics, and metamathematics. There is also a presentation of new results - partly in these areas, but mostly in their synthesis.

Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. This compendium aims to present a comprehensive account of the main approaches and demonstrate the overall unity of the subject.

Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. This compendium aims to present a comprehensive account of the main approaches and demonstrate the overall unity of the subject.

Topos Theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics. This compendium presents a comprehensive account of all the main approaches.

This is a new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader through the basic mathematical and philosophical concepts. Topics like the Bar Theorem, valuation systems and first-order logic have been revised.

This volume presents the philosophical and heuristic framework Cantor developed and explores its lasting effect on modern mathematics. "Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics." -The American Mathematical Monthly

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.

Logic languages are used in computing. Model theory is the mathematical logic which concerns the relationship between mathematical structures and logic languages. The text includes historical information before each topic is introduced. The motivation of the subject and the proofs are explained.

This edited collection bridges the foundations and practice of constructive mathematics. Aimed at academic logicians, mathematicians, philosophers and computer scientists. Including, with contributions from leading researchers, it is up-to-date, highly topical and broad in scope.

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, including proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences.

Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining - or fibring - systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate.

This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.

This updated edition offers the reader an introduction to the field, which focuses on Quine's original work. It includes a revised account of the set theories of Church-Oswald and Mitchell, with permutation models and extensions that preserve power sets.

This book introduces a new unifying framework for logics which makes it particularly suitable for applications. It develops its general theory and illustrates it with applications in logic, computer science, artificial intelligence, and philosophy.

This is a mathematically-oriented advanced textbook in modal logic, a discipline conceived in philosophy and having found applications in mathematics, artificial intelligence, linguistics, and computer science. It presents in a systematic and comprehensive way a wide range of classical and novel methods and results and can be used by a specialist as a reference book.

'Oxford Logic Guide provides comprehensive coverage of a new research area in algebra and model theory. Model theoretical and group theoretical notions are explained in detail, and almost all the known results in the area are included. Aimed at the needs of the graduate student, there are many exercises (with hints) and carefully chosen examples.

An up-to-date, systematic account of the fundamental results of the central areas of model theory (a branch of mathematical logic). The fine structure of models of stable theories is the object of the study, and there are applications to classification theory (such as classifying models of undimensional theories).

The text introduces categories and elementary toposes while requiring little mathematical background. It defines the key concepts and gives complete elementary proofs of theorems, including the fundamental theorem of toposes and the sheafification theorem.

'Many-valued Logics' attempts an elementary exposition of the topics connected with logical many-valueness. It provides readers with a stimulating discussion which focuses on the constructions being "many-valued" at their origin, i.e. those obtained through intended introduction of logical values next to truth and falsity.

Change, Choice and Inference unifies lively and significant strands of research in logic, philosophy, economics and artificial intelligence.

An introduction to the work of the mathematical logician Kurt Godel, which guides the reader through his Theorem of Undecidability and his theories on the completeness of logic, the incompleteness of numbers and the consistency of the axiom of choice.

The fourth edition of a classic book on logic has been thoroughly revised by the author's son. It is a fundamental guide to modern mathematical logic and to the construction of mathematical theories. The first half covers the elements of logic, and the second half covers the applications of logic in theory building. A short biographical sketch of Alfred Tarski is a newly-added section.