Mathematical Logic - Set Theory, Model Theory, Computability, etc

This book gives an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic.

A comprehensive introduction to Automata Theory that uses the novel approach of viewing automata as data structures.

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving.

Addressing the importance of constructing and understanding mathematical proofs, this book introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet.

This book of mathematical 'background' shows how to fill in the mathematical details of the main topics from the course. These proofs are completely rigorous in the sense of modern mathematics - technically bulletproof.

This monograph is a companion to the Author's textbook Elementary Calculus: An Infinitesimal Approach. It can be used as a quick introduction to the infinitesimal approach to calculus for mathematicians, as background material for instructors, or as a text for an undergraduate seminar.

Gentzen's cut-elimination theorem is widely used as a tool for meta-mathematical investigations. It is sometimes claimed however that the theorem and its proof have interest which is independent of these applications and derives from the information they supply about the structure of proofs in general.

This is a short but excellent introduction to modal, temporal, and dynamic logic, etc. It manages to cover, in highly readable style, the basic completeness, decidability, and expressability results in a variety of logics of the three kinds considered.

Logic and the Foundations of Game and Decision Theory is a key venue for presenting research at the intersection of logic, economics and computer science, and the present collection gives a lively and wide-ranging view of an exciting and rapidly growing area.

This book gives a consolidated overview of the research results achieved in the Automata Theory, logics, and infinite games during the past 10 years. Special emphasis is placed on coherent style, complete coverage of all relevant topics, motivation, examples, justification of constructions, and exercises.

This book brings out how sets in algebraic structures can be used to construct the most generalized algebraic structures, like set linear algebra / vector space, set ideals in groups and rings and semigroups, and topological set vector spaces. This sort of study is innovative and will find applications in data handling.

The textbook by Professor Wolfgang Rautenberg is a well-written introduction to the beautiful and coherent subject of mathematical logic. It contains classical material such as logical calculi, beginnings of model theory, and Goedel's incompleteness theorems, as well as some topics motivated by applications, such as a chapter on logic programming.

This book is concerned with an attempt to introduce the infinitesimals and the other 'nonstandard' numbers in a naive, simpleminded way. Nevertheless, the resulting theory is hoped to be mathematically sound, and to be complete within obvious limits.

This first-year calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems. Additional subjects include transcendental functions, series, vectors, partial derivatives, and multiple integrals. 2007 edition.

Addressing the importance of constructing and understanding mathematical proofs, this book introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet.