Product Description: This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs...read more

The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields.

For "baby" analysis with single variable only. Appropriate for one term courses in analysis and advanced calculus. Text starts with a little logic and how to construct a proof. Revision features: material on the topology of the reals has been expanded and divided into two sections. Two optional sections on metric spaces and continuity in metric spaces have been added.

Product Description: The kernel of this book consists of a series of lectures on in?nitary proof theory which I gave during my time at the Westfalische ¨ Wilhelms–Universitat ¨ in Munster ¨ . It was planned as a successor of Springer Lecture Notes in Mathematics 1407...read more

Product Description: When ordinary people-mathematicians among them-take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians...read more

Product Description: In the real world of research mathematics, mathematicians do not know in advance if their assertions are true or false. Extending the Frontiers of Mathematics: Inquiries into proof and argumentation requires students to develop a mature process that will serve them throughout their professional careers, either inside or outside of mathematics...read more

Product Description: Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics...read more

A portrait of the eminent twentieth-century mathematician discusses his groundbreaking theorem of incompleteness, contributions within the famous Vienna circle, relationships with such contemporaries as Albert Einstein, and untimely death as a result of mental instability and self-starvation. Reprint. 20,000 first printing.

Presents a guide to the basic logic of mathematical proofs, describing the steps in construction of a proof and how and why a proof works.

Product Description: This monograph details several important advances in the direction of a practical proofs-as-programs paradigm, which constitutes a set of approaches to developing programs from proofs in constructive logic with applications to industrial-scale, complex software engineering problems...read more

Product Description: 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...read more

Product Description: This book is for researchers in computer science, mathematical logic, and philosophical logic. It shows the state of the art in current investigations of process calculi with mainly two major paradigms at work: linear logic and modal logic...read more

Product Description: The tests will help familiarise students with the format and requirements of the Reading and Writing/Listening and Speaking papers. This book contains exam-format practice tests for Papers 4 and 5 of the Cambridge IGCSE in English as a Second Language...read more

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Product Description: The last twenty years have witnessed an accelerated development of pure and ap­ plied logic, particularly in response to the urgent needs of computer science. Many traditional logicians have developed interest in applications and in parallel a new generation of researchers in logic has arisen from the computer science community...read more

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