# a tour through mathematical logic

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## A Tour Through Mathematical Logic

**Author :**Robert S. Wolf

**ISBN :**0883850362

**Genre :**Mathematics

**File Size :**40. 95 MB

**Format :**PDF, ePub

**Download :**749

**Read :**301

The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gdel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.

## A Tour Through Mathematical Logic

**Author :**Robert S. Wolf

**ISBN :**0883850427

**Genre :**Mathematics

**File Size :**36. 84 MB

**Format :**PDF

**Download :**736

**Read :**984

The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gödel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.

## A Tour Through Mathematical Logic

**Author :**Robert S. Wolf

**ISBN :**0883850362

**Genre :**Mathematics

**File Size :**62. 62 MB

**Format :**PDF

**Download :**689

**Read :**705

The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gdel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.

## A Tour Through Mathematical Logic

**Author :**Robert S. Wolf

**ISBN :**0883850362

**Genre :**Mathematics

**File Size :**21. 80 MB

**Format :**PDF, ePub, Docs

**Download :**776

**Read :**1296

The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gdel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.

## A Profile Of Mathematical Logic

**Author :**Howard DeLong

**ISBN :**9780486139159

**Genre :**Mathematics

**File Size :**40. 47 MB

**Format :**PDF, Mobi

**Download :**566

**Read :**526

This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

## Mathematical Logic

**Author :**Stephen Cole Kleene

**ISBN :**9780486317076

**Genre :**Mathematics

**File Size :**73. 68 MB

**Format :**PDF, ePub, Mobi

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Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

## Handbook Of Mathematical Logic

**Author :**J. Barwise

**ISBN :**0080933645

**Genre :**Mathematics

**File Size :**66. 90 MB

**Format :**PDF, ePub

**Download :**640

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The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

## An Introduction To Mathematical Logic And Type Theory

**Author :**Peter B. Andrews

**ISBN :**9789401599344

**Genre :**Mathematics

**File Size :**57. 26 MB

**Format :**PDF, Docs

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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.

## Perspectives On The History Of Mathematical Logic

**Author :**Thomas Drucker

**ISBN :**9780817647698

**Genre :**Mathematics

**File Size :**67. 14 MB

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This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.

## The Foundations Of Mathematics

**Author :**Kenneth Kunen

**ISBN :**1904987141

**Genre :**Mathematics

**File Size :**60. 74 MB

**Format :**PDF, Kindle

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Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.