# Open Logic Project

Richard Zach, University of Calgary

Andrew Arana, University of Paris

Jeremy Avigad, Carnegie Mellon University

Walter Dean, University of Warwick

Gillian Russell, University of North Carolina

Nicole Wyatt, University of Calgary

Audrey Yap, University of Victoria

Pub Date: 2016

ISBN 13:

Publisher: Independent

## Read This Book

## Conditions of Use

Attribution

CC BY

## Reviews

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## Table of Contents

Sets, Relations, Functions

Chapter 1: Sets

Chapter 2: Relations

Chapter 3: Functions

Chapter 4: The Size of Sets

First-order Logic

Chapter 5: Syntax and Semantics

Chapter 6: Theories and Their Models

Chapter 7: The Sequent Calculus

Chapter 8: Natural Deduction

Chapter 9: The Completeness Theorem

Chapter 10: Beyond First-order Logic

Model Theory

Chapter 11: Basics of Model Theory

Chapter 12: The Interpolation Theorem

Chapter 13: Lindstrorm’s Theorem

Computability

Chapter 14: Recursive Functions

Chapter 15: The Lambda Calculus

Chapter 16: Computability Theory

Turing Machines

Chapter 17: Turing Machine Computations

Chapter 18: Undecidability

Incompleteness

Chapter 19: Arithmetization of Syntax

Chapter 20: Representability in Q

Chapter 21: Theories and Computability

Chapter 22: Incompleteness and Provability

Methods

Chapter 23: Induction

History

Chapter 24: Biographies

Photo Credits

Bibliography

## About the Book

The Open Logic Text is an open-source, collaborative textbook of formal meta-logic and formal methods, starting at an intermediate level (i.e., after an introductory formal logic course). Though aimed at a non-mathematical audience (in particular, students of philosophy and computer science), it is rigorous.

The Open Logic Text is a collaborative project and is under active development. Coverage of some topics currently included may not yet be complete, and many sections still require substantial revision. We plan to expand the text to cover more topics in the future. We also plan to add features to the text, such as a glossary, a list of further reading, historical notes, pictures, better explanations, sections explaining the relevance of results to philosophy, computer science, and mathematics, and more problems and examples. If you find an error, or have a suggestion, please let the project team know.

The project operates in the spirit of open source. Not only is the text freely available, we provide the LaTeX source under the Creative Commons Attribution license, which gives anyone the right to download, use, modify, re-arrange, convert, and re-distribute our work, as long as they give appropriate credit.

## About the Contributors

### Author(s)

**Richard Zach** is a logician working at the University of Calgary (Canada) where he is Professor of Philosophy. He works on the history of logic, the philosophy of logic and mathematics, and mathematical logic. He has recently used the Open Logic Text in a course on Intermediate Logic at McGill University.

**Andrew Arana** is a logician working at the University of Paris 1 Panthéon-Sorbonne (France) where he is maître de conférences (associate professor) of philosophy. He works on the history and philosophy of mathematics and logic. At Paris 1 his logic teaching includes model theory, philosophy of logic, and elementary logic. In his previous appointment as Associate Professor of Philosophy and Mathematics at the University of Illinois at Urbana-Champaign and at other institutions he has taught logic at many different levels as well. He looks forward to using this text in logic courses this academic year.

**Jeremy Avigad** is a logician at Carnegie Mellon University, where he is Professor of Philosophy and Mathematical Sciences. He works in mathematical logic, history and philosophy of mathematics, and formal verification. At Carnegie Mellon, he teaches logic to students in mathematics, computer science, and philosophy, from undergraduate freshmen to advanced graduate students. Sections on computability and incompleteness are based on his notes.

**Walter Dean** is Associate Professor of Philosophy at the University of Warwick (UK). He works in philosophy of mathematics, mathematical and philosophical logic, theoretical computer science, and the philosophy and history of computation. He regularly teaches intermediate and advanced undergraduate logic.

**Gillian Russell** is Professor of Philosophy at the University of North Carolina, Chapel Hill. She writes on the philosophy of language and the philosophy of logic, and often teaches advanced logic courses to philosophers.

**Nicole Wyatt** is a philosopher working at the University of Calgary, where she is also Head of the Department of Philosophy. She works on the philosophy of logic and language, as well as the history of computational theory. She regularly teaches Logic II, as well as Philosophy of Logic, at Calgary. She has used the Open Logic Text twice in Logic II, and contributed material to the sections on first-order logic and Turing computability.

**Audrey Yap** is Associate Professor of Philosophy at the University of Victoria (Canada). She works in epistemic logic, history and philosophy of mathematics, and more recently in feminist epistemology. She teaches logic from the intro level onward.