Table of Contents
Sets, Relations, Functions
Chapter 1: Sets
Chapter 2: Relations
Chapter 3: Functions
Chapter 4: The Size of Sets
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
Chapter 11: Basics of Model Theory
Chapter 12: The Interpolation Theorem
Chapter 13: Lindstrorm’s Theorem
Chapter 14: Recursive Functions
Chapter 15: The Lambda Calculus
Chapter 16: Computability Theory
Chapter 17: Turing Machine Computations
Chapter 18: Undecidability
Chapter 19: Arithmetization of Syntax
Chapter 20: Representability in Q
Chapter 21: Theories and Computability
Chapter 22: Incompleteness and Provability
Chapter 23: Induction
Chapter 24: Biographies
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
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.