Bøger i Studies in Logic and the Foundations of Mathematics serien

Describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. This book presents a detailed picture of the computable sets from the perspective of theoretical computer science. It is suitable for those interested in complexity and computability theory.

Aims to present the fundamental theoretical results concerning inference rules in deductive formal systems. This book focuses on admissible or permissible inference rules; the derivability of the admissible inference rules; the structural completeness of logics; and the bases for admissible and valid inference rules.

Includes a number of applications to logic (in particular Godel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation. This book presents a comprehensive reference for the subject starting from first principles.

The modern theory of algebras of binary relations, reformulated by Tarski as an abstract, algebraic, equational theory of relation algebras, has mathematical significance. This work presents a treatment of the theory of relation algebras and the calculus of relations, which is devoted to a systematic development of the subject.

Relation algebras are algebras arising from the study of binary relations. They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This text uses combinatorial games to study the fundamental notion of representations of relation algebras.

Contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. This book includes the central topics of proof theory. It concludes with articles that deal with topics closely related to computer science.

Aims to study the computational behaviour of many-dimensional modal logics. This book is concerned with providing a mathematical foundation for this discipline, and shows that different applied many-dimensional systems fit in with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.

Presents an introduction to the basic concepts of realizability, a field which has passed several successive phases of abstraction. This title includes a bibliography.

Covers logical systems known as type-free or self-referential. This book shows that there are theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics.

The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as in type theory. The isomorphism has many aspects, even at syntactic level. This book offers an introduction to the proof theory and related aspects of type theory relevant for the isomorphism.

Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras. The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences. The book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras. The publication is a valuable reference for mathematicians and researchers interested in mathematics and logic.

Treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory. This book is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply.

Includes topics of computability theory that have been chosen based on the active research interest associated with them.

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times. This title emphasises on model-theoretic and it concentrates on descriptions of different sound semantics and completeness problem.

Presents results in algebraic research into residuated structures related to substructural logics amd provides an introduction to algebraic logic. This book contains chapters covering universal algebra for logicians, a crash course in nonclassical logics for algebraists, and an introduction to residuated structures.

Describes a program of research in computable structure theory. This book aims to find definability conditions corresponding to bounds on complexity which persist under isomorphism. It includes necessary background material from recursion theory and model theory.

Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.

Attempts to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. This book is useful for logicians, type theorists, category theorists and (theoretical) computer scientists.

Emphasises on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata, explained in an algebraic way. This book is aimed at researchers and students interested in logic in computer science, computer aided verification, and general aspects of automata theory.