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

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.

Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, This book covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.

Introduction to Mathematical Philosophy has been a seminal work for more than nine decades. It gives the general background necessary for any serious discussion on the foundational crisis of mathematics in the beginning of the twentieth century.