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Computability and Logicby George S. Boolos; John P. Burgess; Richard C. Jeffrey
Cambridge University Press 2002; US$ 28.00Now in its fourth edition, this book has become a classic because it covers not simply the staple topics of intermediate logic courses but also a large number of other topics. John Burgess has enhanced the book by adding problems at the end of each chapter and by rewriting chapters. more...
Proof Logic and Formalizationby Michael Detlefsen
Routledge 1992; US$ 135.00A collection of essays from distinguished contributors looking at why it is that mathematical proof is given precedence over other forms of mathematical justification. more...
Tracking Reasonby Jody Azzouni
Oxford University Press 2006; US$ 24.95When 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. This book investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. more...
Lectures on the Curry-Howard Isomorphismby Morten Heine Sørensen; Pawel Urzyczyn
Elsevier 2006; US$ 150.00The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov,... more...
Mathematical Thinking and Writingby Randall Maddox
Elsevier 2001; US$ 107.00The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most... more...
The Nuts and Bolts of Proofsby Antonella Cupillari
Elsevier 2005; US$ 51.95The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. * The "List of Symbols" has been extended. * Set Theory section has been strengthened with more examples and exercises. * Addition of "A Collection of Proofs" more...
Handbook of Computability Theoryby E.R. Griffor
Elsevier 1999; US$ 195.00The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop... more...
Handbook of Proof Theoryby S.R. Buss
Elsevier 1998; US$ 182.00This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science. more...
Computable Structures and the Hyperarithmetical Hierarchyby C.J. Ash; J. Knight
Elsevier 2000; US$ 133.00This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). more...
Computability and Logicby George S. Boolos; John P. Burgess; Richard C. Jeffrey
Cambridge University Press 2007; US$ 26.00Computability and Logic is a classic because of its accessibility to students without a mathematical background. more...