Author: J.D. Monk

Publisher: Springer Science & Business Media

ISBN: 9781468494525

Release Date: 2012-12-06

Genre: Mathematics

From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data." There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.
## An Algebraic Introduction to Mathematical Logic

## A Course in Mathematical Logic

## Fundamentals of Mathematical Logic

## A Course on Mathematical Logic

## Axiomatic Set Theory

## Classical Descriptive Set Theory

## Mathematical Logic and Model Theory

## Introduction to Axiomatic Set Theory

## Notes on Logic and Set Theory

## A Course in Model Theory

## An Introduction to Mathematical Logic

## An Introduction to Mathematical Logic and Type Theory

Author: Peter B. Andrews

Publisher: Springer Science & Business Media

ISBN: 9789401599344

Release Date: 2013-04-17

Genre: Mathematics

In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
Publisher: Springer Science & Business Media

ISBN: 9789401599344

Release Date: 2013-04-17

Genre: Mathematics