Books

Mathematical Logic

Introductory LogicAuthors
Mathematical Introduction to LogicH. B. Enderton
Modern Mathematical LogicJ. Mileti
Beginner's Guide to LogicR. M. Smullyan
Computability TheoryB. Cooper
Computability: an introductionN. Cutland
Computability Theory: an introductionH. B. Enderton
Computability TheoryAuthors
Classical Recursion Theory Vol I, IIP. G. Odifreddi
Turing Computability - Theory and ApplicationsR. I. Soare
Recursively Enumerable Sets and DegreesR. I. Soare
Recursive Functions and ComputabilityH. Rogers, Jr.
Computability TheoryB. Cooper
Computability: an introductionN. Cutland
Recursion theory for metamathematicsR. M. Smullyan
Algorithmic RandomnessAuthors
Algorithmic Randomness and ComplexityDowney, Hirschfeldt
Computability and RandomnessA. Nies
Kolmogorov Complexity and RandomnessShen, Uspensky, Vereshchagin
Kolmogorov Complexity and ApplicationsP. Vitanyi

Specialized

Degrees and HierarchiesAuthors
Recursion-Theoretic HierarchiesP. Hinman
Recursively Enumerable Sets and DegreesR. I. Soare
Degrees of Unsolvability: Structure and TheoryR. L. Epstein
Degrees of UnsolvabilityM. Lerman
Degrees of UnsolvabilityJ. R. Shoenfield
Higher recursion theoryAuthors
Higher Recursion TheoryG. E. Sacks
Recursion TheoryC. T. Chong, L. Yu
Reverse Math and StructuresAuthors
Slicing the truth: Reverse MathematicsD. R. Hirschfeldt
Reverse Mathematics: proofs from the inside outJ. Stillwell
Subsystems of Second Order ArithmeticS. Simpson
Computable Structure TheoryA. Montalban
Computable Structures and Hyperarithmetical HierarchyC. J. Ash, J. Knight

General reading

  • Weapons of Math Destruction
  • One, Two, Three...Infinity Zero
  • Innumeracy: Mathematical Illiteracy
  • Man Who Knew Infinity: Ramanujan
  • How to Lie with Statistics
  • Mathematical proofs and Discovery
  • Code Book: The Science of Secrecy
  • Letters to a Young Mathematician
  • Weapons of Math Destruction
  • e: the Story of a Number
  • One, Two, Three...Infinity
  • Zero: Biography of a Dangerous Idea
  • Innumeracy: Mathematical Illiteracy
  • The Man Who Knew Infinity: Ramanujan
  • The Man of Numbers: Fibonacci's Revolution
  • Beyond Infinity - Limits of Mathematics
  • How to Lie with Statistics
  • Gödel's Incompleteness Theorems
  • Guided Tour Through Gödel’s Proof
  • Rise of Mathematical Logic