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

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.

Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume is the first ever collection devoted to the field of proof-theoretic semantics.

This open access book investigates the role played by identity of proofs in proof-theoretic semantics. It develops a conception of proof-theoretic semantics as primarily concerned with the relationship between proofs (understood as abstract entities) and derivations (the linguistic representations of proofs).

There are many wonderful introductory texts on mathematical logic, but there are also many not-so-useful books. So how do you find your way around the very large literature old and new, and how do you choose what to read? Beginning Mathematical Logic provides the necessary guide. It introduces the core topics and recommends the best books for studying these topics enjoyably and effectively. This will be an invaluable resource both for those wanting to teach themselves new areas of logic and for those looking for supplementary reading before or during a university course.

This book explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.

This book is an Hyper-textbook for students in mathematical logic and foundations of mathematics. Contents: Platonism, intuition and the nature of mathematics; Axiomatic Set Theory; First Order Arithmetic; Hilbert's Tenth Problem; Incompleteness Theorems; Around Goedel's Theorem.

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory.

Deals with the mathematical background of the application to computer science of aspects of logic on typed lambda calculus (namely the correspondence between propositions and types). Treats both the traditional logic material, and its prospective application to computer science.