Computability
eBook - PDF

Computability

Computable Functions, Logic, and the Foundations of Mathematics

  1. 382 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Computability

Computable Functions, Logic, and the Foundations of Mathematics

About this book

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".

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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 Mathematik & Logik in der Mathematik. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Table of Contents
  2. Preface
  3. 1 Paradoxes
  4. 2 What Do the Paradoxes Mean?
  5. 3 Whole Numbers
  6. 4 Functions
  7. 5 Proofs
  8. 6 Infinite Collections?
  9. 7 Hilbert "On the Infinite"
  10. 8 Computability
  11. 9 Turing Machines
  12. 10 The Most Amazing Fact and Church's Thesis
  13. 11 Primitive Recursive Functions
  14. 12 The Grzegorczyk Hierarchy
  15. 13 Multiple Recursion
  16. 14 The Least Search Operator
  17. 15 Partial Recursive Functions
  18. 16 Numbering the Partial Recursive Functions
  19. 17 Listability
  20. 18 Turing Machine Computable = Partial Recursive
  21. 19 Propositional Logic
  22. 20 An Overview of First-Order Logic and Gödel's Theorems
  23. 21 First-Order Arithmetic
  24. 22 Functions Representable in Formal Arithmetic
  25. 23 The Undecidability of Arithmetic
  26. 24 The Unprovability of Consistency
  27. 25 Church's Thesis
  28. 26 Constructivist Views of Mathematics
  29. 27 Mathematics as Modeling
  30. Computability and Undecidability—A Timeline
  31. Bibliography
  32. Glossary and Index of Notation
  33. Index