The Structure of Proof
The Structure of Proof

Author: Michael L. O'Leary

Publisher:

Published: 2002

Total Pages: 440

ISBN-13:

DOWNLOAD EBOOK

For a one-semester freshman or sophomore level course on the fundamentals of proof writing or transition to advanced mathematics course. Rather than teach mathematics and the structure of proofs simultaneously, this text first introduces logic as the foundation of proofs and then demonstrates how logic applies to mathematical topics. This method ensures that the students gain a firm understanding of how logic interacts with mathematics and empowers them to solve more complex problems in future math courses.

The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal
The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

Author: W. Hugh Woodin

Publisher: Walter de Gruyter

Published: 2013-02-01

Total Pages: 944

ISBN-13: 3110804735

DOWNLOAD EBOOK

The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

Models and Ultraproducts
Models and Ultraproducts

Author: A. B. Slomson

Publisher: Dover Publications

Published: 2013-12-20

Total Pages: 336

ISBN-13: 9780486788630

DOWNLOAD EBOOK

This first-year graduate text assumes only an acquaintance with set theory to explore homogeneous universal models, saturated structure, extensions of classical first-order logic, and other topics. 1974 edition.

The Lambda Calculus
The Lambda Calculus

Author: H.P. Barendregt

Publisher: North Holland

Published: 1984

Total Pages: 648

ISBN-13:

DOWNLOAD EBOOK

The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.

Protoalgebraic Logics
Protoalgebraic Logics

Author: Janusz Czelakowski

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 456

ISBN-13: 9401728070

DOWNLOAD EBOOK

The main aim of this book is to present recent ideas in logic centered around the notion of a consequence operation. We wish to show these ideas in a factually and materially connected way, i.e., in the form of a consistent theory derived from several simple assumptions and definitions. These ideas have arisen in many research centers. The thorough study of their history can certainly be an exciting task for the historian of logic; in the book this aspect of the theory is being played down. The book belongs to abstract algebraic logic, the area of research that explores to a large extent interconnections between algebra and logic. The results presented here concern logics defined in zero-order languages (Le., quantifier-free sentential languages without predicate symbols). The reach of the theory expounded in the book is, in fact, much wider. The theory is also valid for logics defined in languages of higer orders. The problem of transferring the theory to the level of first-order languages has been satisfactorily solved and new ideas within this area have been put forward in the work of Blok and Pigozzi [1989].

Boolean Functions
Boolean Functions

Author: Yves Crama

Publisher: Cambridge University Press

Published: 2011-05-16

Total Pages: 711

ISBN-13: 1139498630

DOWNLOAD EBOOK

Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.