محاسبه پذیری: توابع محاسبه پذیر، منطق و بنیان های ریاضیات ۲۰۱۸
Computability: Computable Functions, Logic, and the Foundations of Mathematics 2018

1. Table of Contents

2. 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

30. Computability and Undecidability—A Timeline

31. Bibliography

32. Glossary and Index of Notation

33. Index