Now in a new edition!--the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".
eBook - PDF
Computability
Computable Functions, Logic, and the Foundations of Mathematics
- 382 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Computability
Computable Functions, Logic, and the Foundations of Mathematics
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Table of contents
- Table of Contents
- Preface
- 1 Paradoxes
- 2 What Do the Paradoxes Mean?
- 3 Whole Numbers
- 4 Functions
- 5 Proofs
- 6 Infinite Collections?
- 7 Hilbert "On the Infinite"
- 8 Computability
- 9 Turing Machines
- 10 The Most Amazing Fact and Church's Thesis
- 11 Primitive Recursive Functions
- 12 The Grzegorczyk Hierarchy
- 13 Multiple Recursion
- 14 The Least Search Operator
- 15 Partial Recursive Functions
- 16 Numbering the Partial Recursive Functions
- 17 Listability
- 18 Turing Machine Computable = Partial Recursive
- 19 Propositional Logic
- 20 An Overview of First-Order Logic and Gödel's Theorems
- 21 First-Order Arithmetic
- 22 Functions Representable in Formal Arithmetic
- 23 The Undecidability of Arithmetic
- 24 The Unprovability of Consistency
- 25 Church's Thesis
- 26 Constructivist Views of Mathematics
- 27 Mathematics as Modeling
- Computability and Undecidability—A Timeline
- Bibliography
- Glossary and Index of Notation
- Index
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Yes, you can access Computability by Richard L Epstein,Walter A Carnielli in PDF and/or ePUB format, as well as other popular books in Mathematics & Logic in Mathematics. We have over one million books available in our catalogue for you to explore.